238431355 plaxis-tutorial-manual

PLAXIS 3D

Tutorial Manual

2013

Build 6448

TABLE OF CONTENTS

TABLE OF CONTENTS

1 Foundation in overconsolidated clay 71.1 Case A: Rigid foundation 81.2 Case B: Raft foundation 201.3 Case C: Pile-Raft foundation 27

2 Excavation in sand 332.1 Geometry 342.2 Mesh generation 392.3 Performing calculations 392.4 Viewing the results 42

3 Loading of a suction pile 473.1 Geometry 473.2 Mesh generation 503.3 Performing calculations 513.4 Viewing the results 52

4 Construction of a road embankment 534.1 Geometry 534.2 Mesh generation 574.3 Performing calculations 584.4 Viewing the results 614.5 Safety analysis 644.6 Using drains 67

5 Phased excavation of a shield tunnel 695.1 Geometry 695.2 Mesh generation 785.3 Performing calculations 795.4 Viewing the results 86

6 Rapid drawdown analysis 876.1 Geometry 876.2 Mesh generation 896.3 Performing calculations 906.4 Viewing the results 95

7 Dynamic analysis of a generator on an elastic foundation 977.1 Geometry 977.2 Mesh generation 1007.3 Performing calculations 1017.4 Viewing the results 104

8 Free vibration and earthquake analysis of a building 1078.1 Geometry 1078.2 Mesh generation 1138.3 Performing calculations 1138.4 Viewing the results 115

PLAXIS 3D 2013 | Tutorial Manual 3

TUTORIAL MANUAL

Appendix A - Menu tree 119

Appendix B - Calculation scheme for initial stresses due to soil weight 123

4 Tutorial Manual | PLAXIS 3D 2013

INTRODUCTION

INTRODUCTION

PLAXIS is a finite element package that has been developed specifically for the analysisof deformation and stability in geotechnical engineering projects. The simple graphicalinput procedures enable a quick generation of complex finite element models, and theenhanced output facilities provide a detailed presentation of computational results. Thecalculation itself is fully automated and based on robust numerical procedures. Thisconcept enables new users to work with the package after only a few hours of training.

Though the various tutorials deal with a wide range of interesting practical applications,this Tutorial Manual is intended to help new users become familiar with PLAXIS 3D. Thetutorials should therefore not be used as a basis for practical projects.

Users are expected to have a basic understanding of soil mechanics and should be ableto work in a Windows environment. It is strongly recommended that the tutorials arefollowed in the order that they appear in the manual.

The Tutorial Manual does not provide theoretical background information on the finiteelement method, nor does it explain the details of the various soil models available in theprogram. The latter can be found in the Material Models Manual, as included in the fullmanual, and theoretical background is given in the Scientific Manual. For detailedinformation on the available program features, the user is referred to the ReferenceManual. In addition to the full set of manuals, short courses are organised on a regularbasis at several places in the world to provide hands-on experience and backgroundinformation on the use of the program.


TUTORIAL MANUAL


FOUNDATION IN OVERCONSOLIDATED CLAY

1 FOUNDATION IN OVERCONSOLIDATED CLAY

In this chapter a first application of PLAXIS 3D is considered, namely the settlement of afoundation in clay. This is the first step in becoming familiar with the practical use of theprogram.

The general procedures for the creation of a geometry, the generation of a finite elementmesh, the execution of a finite element calculation and the evaluation of the output resultsare described here in detail. The information provided in this tutorial will be utilised in thefollowing tutorials. Therefore, it is important to complete this first tutorial beforeattempting any further tutorial examples.

18.0 m

75.0 m

75.0 mBuilding

Clay

x

x

y

z

z = 0z = -2

z = -40

40.0 m

Figure 1.1 Geometry of a square building on a raft foundation

GEOMETRY

This exercise deals with the construction and loading of a foundation of a square buildingin a lightly overconsolidated lacustrine clay. Below the clay layer there is a stiff rock layerthat forms a natural boundary for the considered geometry. The rock layer is not includedin the geometry; instead an appropriate boundary condition is applied at the bottom of theclay layer. The purpose of the exercise is to find the settlement of the foundation.

The building consists of a basement level and 5 floors above the ground level (Figure1.1). To reduce calculation time, only one-quarter of the building is modelled, usingsymmetry boundary conditions along the lines of symmetry. To enable any possible


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mechanism in the clay and to avoid any influence of the outer boundary, the model isextended in both horizontal directions to a total width of 75 m.

The model is considered in three different cases:

Case A: The building is considered very stiff and rough. The basement is simulated bymeans of non-porous linear elastic volume elements.

Case B: The structural forces are modelled as loads on a raft foundation.

Case C: Embedded piles are included in the model to reduce settlements.

1.1 CASE A: RIGID FOUNDATION

In this case, the building is considered to be very stiff. The basement is simulated byterms of non-porous linear elastic volume elements. The total weight of the basementcorresponds to the total permanent and variable load of the building. This approach leadsto a very simple model and is therefore used as a first exercise, but it has somedisadvantages. For example it does not give any information about the structural forces inthe foundation.

Objectives:

• Starting a new project.

• Creation of soil stratigraphy using a single borehole.

• Creation of material data sets.

• Creation of volumes using Create surface and Extrude tools.

• Assigning material.

• Local mesh refinement.

• Generation of mesh.

• Generating initial stresses using the K0 procedure.

• Defining a Plastic calculation.

1.1.1 GEOMETRY INPUT

• Start the PLAXIS 3D program. The Quick select dialog box will appear in which youcan select an existing project or create a new one (Figure 1.2).

• Click Start a new project. The Project properties window appears, consisting ofProject and Model tabsheets.

Project properties

The first step in every analysis is to set the basic parameters of the finite element model.This is done in the Project properties window. These properties include the description ofthe problem, the basic units and the size of the draw area.



Figure 1.2 Quick select dialog box

To enter the appropriate properties for the foundation calculation follow these steps:

• In the Project tabsheet, enter "Tutorial 1" as the Title of the project and type"Settlements of a foundation" in the Comments box (Figure 1.3).

Figure 1.3 Project tabsheet of the Project properties window

• Proceed to the Model tabsheet by clicking either the Next button or the Model tab(Figure 1.4).

• Keep the default units in the Units box (Length = m; Force = kN; Time = day ).

• The General box indicates a fixed gravity of 1.0 G, in the vertical direction downward(-z). The value of the acceleration of gravity (1.0 G) can be specified in the Earthgravity box. This should be kept to the default value of 9.810 m/s2 for this exercise.In the γwater box the unit weight of water can be defined. Keep this to the defaultvalue of 10 kN/m3.

• Define the limits for the soil contour as xmin = 0, xmax = 75, ymin = 0 and ymax = 75 inthe Contour group box.

• Click the OK button to confirm the settings.

Hint: In case of a mistake or for any other reason that the project properties needto be changed, you can access the Project properties window by selectingthe corresponding option in the File menu.


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Figure 1.4 Model tabsheet of the Project properties window

Definition of soil stratigraphy

When you click the OK button the Project properties window will close and the Soil modeview will be shown. Information on the soil layers is entered in boreholes.

Boreholes are locations in the draw area at which the information on the position of soillayers and the water table is given. If multiple boreholes are defined, PLAXIS 3D willautomatically interpolate between the boreholes, and derive the position of the soil layersfrom the borehole information.

Hint: PLAXIS 3D can also deal with layers that are discontinuous, i.e. only locallypresent in the model area. See Section 4.2.2 of the Reference Manual formore information.

In the current example, only one soil layer is present, and only a single borehole isneeded to define the soil stratigraphy. In order to define the borehole, follow these steps:

Click the Create borehole button in the side toolbar to start defining the soilstratigraphy. Click on position (0 0 0) in the geometry. A borehole will be located at(x , y ) = (0 0). The Modify soil layers window will appear.

• In the Modify soil layers window add a soil layer by clicking on the Add button. Keepthe top boundary of the soil layer at z = 0 and set the bottom boundary to z = −40m.

• Set the Head value in the borehole column to −2 m (Figure 1.5).

The creation of material data sets and their assignment to soil layers is described in thefollowing section.

1.1.2 MATERIAL DATA SETS

In order to simulate the behaviour of the soil, a suitable material model and appropriatematerial parameters must be assigned to the geometry. In PLAXIS soil properties arecollected in material data sets and the various data sets are stored in a materialdatabase. From the database, a data set can be assigned to one or more clusters. Forstructures (like beams, plates, etc.) the system is similar, but different types of structures



Figure 1.5 Modify soil layers window

have different parameters and therefore different types of data sets.

PLAXIS 3D distinguishes between material data sets for Soils and interfaces, Plates,Geogrids, Beams, Embedded Piles and Anchors. Before the mesh can be generatedmaterial data sets have to be assigned to all soil volumes and structures.

Open the Material sets window by clicking the Materials button in the Modify soillayers window.

Hint: In the case that the Modify soil layers window was closed by mistake, it canbe re-opened by double-clicking the borehole in the draw area or by selectingthe Modify soil layers option from the Soil menu.

• Click the New button in the lower part of the Material sets window. The Soil windowwill appear. It contains five tabsheets: General, Parameters, Flow parameters,Interfaces and Initial.

• In the Material set box of the General tabsheet (Figure 1.6), write "Lacustrine Clay"in the Identification box.

• Select Mohr-Coulomb as the material model from the Material model drop-downmenu and Drained from the Drainage type drop-down menu.

• Enter the unit weights in the General properties box according to the material dataas listed in Table 1.1. Keep the unmentioned Advanced parameters as their defaultvalues.

• Click the Next button or click the Parameters tab to proceed with the input of modelparameters. The parameters appearing on the Parameters tabsheet depend on theselected material model (in this case the Mohr-Coulomb model). The Mohr-Coulomb


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Figure 1.6 General tabsheet of the Soil and interfaces data set window

Table 1.1 Material properties

Parameter Name Lacustrine clay Building Unit

General

Material model Model Mohr-Coulomb Linear elastic −Drainage type Type Drained Non-porous −Unit weight above phreatic level γunsat 17.0 50 kN/m3

Unit weight below phreatic level γsat 18.0 − kN/m3

Parameters

Young's modulus (constant) E ' 1 · 104 3 · 107 kN/m2

Poisson's ratio ν ' 0.3 0.15 −Cohesion (constant) c'ref 10 − kN/m2

Friction angle ϕ' 30.0 − ◦

Dilatancy angle ψ 0.0 − ◦

Initial

K0 determination − Automatic Automatic −Lateral earth pressure coefficient K0 0.5000 1.000 −

model involves only five basic parameters (E ', ν ', c',ϕ',ψ'). See the Material ModelsManual for a detailed description of the different soil models and their correspondingparameters.

• Enter the model parameters E ', ν ', c'ref , ϕ' and ψ of Lacustrine clay according toTable 1.1 in the corresponding boxes of the Parameters tabsheet (Figure 1.7).



Figure 1.7 Parameters tabsheet of the Soil and interfaces data set window

• No consolidation will be considered in this exercise. As a result, the permeability ofthe soil will not influence the results and the Flow parameters window can beskipped.

• Since the geometry model does not include interfaces, the Interfaces tab can beskipped.

• Click the Initial tab and check that the K0 determination is set to Automatic. In thatcase K0 is determined from Jaky's formula: K0 = 1− sinϕ.

• Click the OK button to confirm the input of the current material data set. The createddata set appears in the tree view of the Material sets window.

• Drag the set Lacustrine clay from the Material sets window (select it and hold downthe left mouse button while moving) to the graph of the soil column on the left handside of the Modify soil layers window and drop it there (release the left mousebutton).

Hint: Notice that the cursor changes shape to indicate whether or not it is possibleto drop the data set. Correct assignment of the data set to the soil layer isindicated by a change in the colour of the layer.

The building is modelled by a linear elastic non-porous material. To define this data set,follow these steps:

• Click the New button in the Material sets window.

• In the Material set box of the General tabsheet, write "Building" in the Identificationbox.

• Select Linear elastic as the material model from the Material model drop-downmenu and Non-porous from the Drainage type drop-down menu.


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• Enter the unit weight in the General properties box according to the material data setas listed in Table 1.1. This unit weight corresponds to the total permanent andvariable load of the building.

• Click the Next button or click the Parameters tab to proceed with the input of themodel parameters. The linear elastic model involves only two basic parameters (E ',ν ').

• Enter the model parameters of Table 1.1 in the corresponding edit boxes of theParameters tabsheet.

• Click the OK button to confirm the input of the current material data set. The createddata set will appear in the tree view of the Material sets window, but it is not directlyused.

• Click the OK button to close the Material sets window.

• Click the OK button to close the Modify soil layers window.

Hint: PLAXIS 3D distinguishes between a project database and a global databaseof material sets. Data sets may be exchanged from one project to anotherusing the global database. The global database can be shown in the Materialsets window by clicking the Show global button. The data sets of all tutorialsin the Tutorial Manual are stored in the global database during the installationof the program.

1.1.3 DEFINITION OF STRUCTURAL ELEMENTS

The structural elements are created in the Structures mode of the program. Click theStructures button to proceed with the input of structural elements. To model the building:

Click the Create surface button. Position the cursor at the coordinate (0 0 0). Checkthe cursor position displayed in the cursor position indicator. As you click, the firstsurface point of the surface is defined.

• Define three other points with coordinates (0 18 0), (18 18 0), (18 0 0) respectively.Press the right mouse button or <Esc> to finalize the definition of the surface. Notethat the created surface is still selected and displayed in red.

Click the Extrude object button to create a volume from the surface.

• Change the z value to -2 in the Extrude window (Figure 1.8). Click the Apply buttonto close the window.

Click the Select button. Select the created surface using the right mouse button.Select Delete from the appearing menu. This will delete the surface but the buildingvolume is retained.

The building volume, as well as the corresponding material data sets have now beencreated.



Figure 1.8 Extrude window

1.1.4 MESH GENERATION

The model is complete. In order to proceed to the Mesh mode click the Mesh tab.PLAXIS 3D allows for a fully automatic mesh generation procedure, in which thegeometry is divided into volume elements and compatible structure elements, ifapplicable. The mesh generation takes full account of the position of the geometryentities in the geometry model, so that the exact position of layers, loads and structures isaccounted for in the finite element mesh. A local refinement will be considered in thebuilding volume. To generate the mesh, follow these steps:

Click the Refine mesh button in the side toolbar and click the created buildingvolume to refine the mesh locally. It will colour green.

Figure 1.9 The indication of the local refinement in the model

Click the Generate mesh button in the side toolbar or select the Generate meshoption in the Mesh menu. Change the Element distribution to Coarse in the Meshoptions window (Figure 1.10) and click OK to start the mesh generation.

As the mesh is generated, click the View mesh button. A new window is openeddisplaying the generated mesh (Figure 1.11).

Click the Close button to go back to the Mesh mode of the Input program.


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Figure 1.10 Mesh options window

Figure 1.11 Generated mesh in the Output window

Hint: By default, the Element distribution is set to Medium. The Elementdistribution setting can be changed in the Mesh options window. In addition,options are available to refine the mesh globally or locally (Section 7.1 ofReference Manual).

» The finite element mesh has to be regenerated if the geometry is modified.» The automatically generated mesh may not be perfectly suitable for the

intended calculation. Therefore it is recommended that the user inspects themesh and makes refinements if necessary.

1.1.5 PERFORMING CALCULATIONS

Once the mesh has been generated, the finite element model is complete. Click Stagedconstruction to proceed with the definition of calculation phases.

Initial conditions

The 'Initial phase' always involves the generation of initial conditions. In general, the initialconditions comprise the initial geometry configuration and the initial stress state, i.e.effective stresses, pore pressures and state parameters, if applicable. The initial waterlevel has been entered already in the Modify soil layers window. This level is taken intoaccount to calculate the initial effective stress state. It is therefore not needed to enter theWater levels mode.



When a new project has been defined, a first calculation phase named "Initial phase", isautomatically created and selected in the Phases explorer (Figure 1.12). All structuralelements and loads that are present in the geometry are initially automatically switchedoff; only the soil volumes are initially active.

Figure 1.12 Phases explorer

In this tutorial lesson the properties of the Initial phase will be described. This part of thetutorial gives an overview of the options to be defined even though the default values ofthe parameters are used.

The Phases window (Figure 1.13) is displayed by clicking the Edit phase button orby double clicking on the phase in the Phases explorer.

Figure 1.13 The Phases window for Initial phase

By default the K0 procedure is selected as Calculation type in the General subtreeof the Phases window. This option will be used in this project to generate the initialstresses.

The Staged construction option is selected as the Loading type. This is the onlyoption available for the K0 procedure.

The Phreatic option is selected by default as the Pore pressure calculation type.

• The other default options in the Phases window will be used as well in this tutorial.Click OK to close the Phases window.

• In the Model explorer extend the Model conditions subtree.

• Extend the Water subtree. The water level generated according to the Head valueassigned to boreholes in the Modify soil layers window (BoreholeWaterLevel_1) isautomatically assigned to GlobalWaterLevel.

• Make sure that all the soil volumes in the project are active and the materialassigned to them is Lacustrine clay.


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Hint: The K0 procedure may only be used for horizontally layered geometries witha horizontal ground surface and, if applicable, a horizontal phreatic level.See Section 7.3 of the Reference Manual for more information on the K0procedure.

Construction stage

After the definition of the initial conditions, the construction of the building can bemodelled. This will be done in a separate calculation phase, which needs to be added asfollows:

Click the Add button in the Phases explorer. A new phase, named Phase_1 will beadded in the Phases explorer.

• Double-click Phase_1 to open the Phases window.

• In the ID box of the General subtree, write (optionally) an appropriate name for thenew phase (for example "Building").

• The current phase starts from Initial phase, which contains the initial stress state.The default options and values assigned are valid for this phase (Figure 1.14).

Figure 1.14 The Phases window for Building phase

• Click OK to close the Phases window.

• Right-click the building volume as created in Section 1.1.3. From the Set materialoption in the appearing menu select the Building option. The 'Building' data set hasnow been assigned to the building volume.

Hint: Calculation phases may be added, inserted or deleted using the Add, Insertand Delete buttons in the Phases explorer or in the Phases window.

Execution of calculation

All calculation phases (two phases in this case) are marked for calculation (indicated by ablue arrow). The execution order is controlled by the Start from phase parameter.



Click the Calculate button to start the calculation process. Ignore the warning thatno nodes and stress points have been selected for curves. During the execution of acalculation, a window appears which gives information about the progress of theactual calculation phase (Figure 1.15).

Figure 1.15 Active task window displaying the calculation progress

The information, which is continuously updated, shows, amongst others, the calculationprogress, the current step number, the global error in the current iteration and the numberof plastic points in the current calculation step. It will take a few seconds to perform thecalculation. When a calculation ends, the window is closed and focus is returned to themain window.

The phase list in the Phases explorer is updated. A successfully calculated phase isindicated by a check mark inside a green circle.

Save the project before viewing results.

Viewing calculation results

Once the calculation has been completed, the results can be displayed in the Outputprogram. In the Output program, the displacement and stresses in the full threedimensional model as well as in cross sections or structural elements can be viewed.The computational results are also available in tabular form. To view the current results,follow these steps:

• Select the last calculation phase (Building) in the Phases explorer tree.

Click the View calculation results button in the side toolbar to open the Outputprogram. The Output program will, by default, show the three dimensional deformedmesh at the end of the selected calculation phase. The deformations are scaled toensure that they are clearly visible.


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• Select Total Displacements→ |u| from the Deformations menu. The plot showscolour shadings of the total displacements (Figure 1.16).

• A legend is presented with the displacement values at the colour boundaries. Whenthe legend is not present, select the Legend option from the View menu to display it.

In the Output window click the Iso surfaces button to display the areas having thesame displacement.

Figure 1.16 Shadings of Total displacements at the end of the last phase

Hint: In addition to the Total displacements, the Deformations menu allows for thepresentation of Incremental displacements and Phase displacements.

» The incremental displacements are the displacements that occurred in onecalculation step (in this case the final step). Incremental displacements maybe helpful in visualising failure mechanisms.

» Phase displacements are the displacements that occurred in one calculationphase (in this case the last phase). Phase displacements can be used toinspect the impact of a single construction phase, without the need to resetdisplacements to zero before starting the phase.

1.2 CASE B: RAFT FOUNDATION

In this case, the model is modified so that the basement consists of structural elements.This allows for the calculation of structural forces in the foundation. The raft foundationconsists of a 50 cm thick concrete floor stiffened by concrete beams. The walls of thebasement consist of 30 cm thick concrete. The loads of the upper floors are transferredto the floor slab by a column and by the basement walls. The column bears a load of



11650 kN and the walls carry a line load of 385 kN/m, as sketched in Figure 1.17.

12.0 m12.0 m

6.0 m6.0 m

385 kN/m385 kN/m

11650 kN

5.3 kN/m2

Figure 1.17 Geometry of the basement

In addition, the floor slab is loaded by a distributed load of 5.3 kN/m2. The properties ofthe clay layer will be modified such that stiffness of the clay will increase with depth.

Objectives:

• Saving project under a different name.

• Modifying existing data sets.

• Defining a soil stiffness that increases with depth.

• Modelling of plates and defining material data set for plates.

• Modelling of beams and defining material data set for beams.

• Assigning point loads.

• Assigning line loads.

• Assigning distributed loads to surfaces.

• Deleting phases.

• Activation and deactivation of soil volumes.

• Activation and deactivation of structural elements.

• Activation of loads.

• Zooming in Output.

• Drawing cross sections in Output.

• Viewing structural output.

Geometry input

The geometry used in this exercise is the same as the previous one, except thatadditional elements are used to model the foundation. It is not necessary to create a newmodel; you can start from the previous model, store it under a different name and modifyit. To perform this, follow these steps:

Start the PLAXIS 3D program. The Quick select dialog box will appear in which theproject of case A should be selected.

• Select the Save project as option in the File menu to save the project under a


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different name (e.g. "Tutorial 1b").

The material set for the clay layer has already been defined. To modify this material set totake into account the stiffness of the soil increasing with depth, follow these steps:

Open the Material sets window by clicking the Show materials button.

• Make sure that the option Soil and interfaces is selected as Set type.

• Select the Lacustrine clay material set and click the Edit button.

• In the Parameters tabsheet, change the stiffness of the soil E ' to 5000 kN/m2.

• Enter a value of 500 in the E 'inc box in the Advanced parameters. Keep the defaultvalue of 0.0 m for zref . Now the stiffness of the soil is defined as 5000 kN/m2 atz = 0.0 m and increases with 500 kN/m2 per meter depth.

• Click OK to close the Soil window.

• Click OK to close the Material sets window.

Definition of structural elements

Proceed to the Structures mode to define the structural elements that compose thebasement.

Click the Selection button.

• Right-click the volume representing the building. Select the Decompose intosurfaces option from the appearing menu.

• Delete the top surface by selecting it and pressing the <Delete> key.

Select the volume representing the building. Click the visualisation toggle in theSelection explorer to hide the volume.

• Right-click the bottom surface of the building. Select the Create plate option fromthe appearing menu.

• Assign plates to the two vertical basement surfaces that are inside the model.Delete the remaining two vertical surfaces at the model boundaries.

Hint: Multiple entities can be selected by holding the <Ctrl> button pressed whileclicking on the entities.

» A feature can be assigned to multiple similar objects the same way as to asingle selection.

Open the material data base and set the Set type to Plates.

• Create data sets for the basement floor and for the basement walls according toTable 1.2.

• Drag and drop the data sets to the basement floor and the basement wallsaccordingly. It may be needed to move the Material sets window by clicking at itsheader and dragging it.




Figure 1.18 Location of plates in the project

Table 1.2 Material properties of the basement floor and basement walls

Parameter Name Basement floor Basement wall Unit

Thickness d 0.5 0.3 mWeight γ 15 15.5 kN/m3

Type of behaviour Type Linear, isotropic Linear, isotropic −Young's modulus E1 3 · 107 3 · 107 kN/m2

Poisson's ratio ν12 0.15 0.15 −

Hint: When specifying a unit weight, please consider the fact that the element itselfdoes not occupy any volume and overlaps with the soil elements. Hence, itmight be considered to subtract the unit soil weight from the real unit weightof the plate, beam or embedded pile material in order to compensate for theoverlap. For partially overlapping plates, beams or embedded piles thereduction of the unit weight should be proportional.

• Right-click the bottom of the surface of the building volume and select the Createsurface load option from the appearing menu. The actual value of the load can beassigned in the Structures mode as well as when the calculation phases will bedefined (Phase definition mode). In this example, the value will be assigned in thePhase definition modes.

Click the Create line button in the side toolbar.

Select the Create line load option from the additional tools displayed.

• Click the command input area, type "0 18 0 18 18 0 18 0 0 " and press <Enter>.Line loads will now be defined on the basement walls. The defined values are thecoordinates of the three points of the lines. Click the right mouse button to stopdrawing line loads.

Click the Create line button in the side toolbar.

Select the Create beam option from the additional tools displayed.

• Click on (6 6 0) to create the first point of a vertical beam. Keep the <Shift> keypressed and move the mouse cursor to (6 6 -2). Note that while the <Shift> key ispressed the cursor will move only vertically. As it can be seen in the cursor positionindicator, the z coordinate changes, while x and y coordinates will remain the same.Click on (6 6 -2) to define the second point of the beam. To stop drawing click the


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right mouse button.

• Create horizontal beams from (0 6 -2) to (18 6 -2) and from (6 0 -2) to (6 18 -2).

Hint: By default, the cursor is located at z=0. To move in the vertical direction,keep the <Shift> key pressed while moving the mouse.

Open the material data base and set the Set type to Beams.

• Create data sets for the horizontal and for the vertical beams according to Table 1.3.Assign the data set to the corresponding beam elements by drag and drop.

Table 1.3 Material properties of the basement column and basement beams

Parameter Name Basement column Basement beam Unit

Cross section area A 0.49 0.7 m2

Volumetric weight γ 24.0 6.0 kN/m3

Type of behaviour Type Linear Linear −Young's modulus E 3 · 107 3 · 107 kN/m2

Moment of Inertia I3 0.020 0.058 m4

I2 0.020 0.029 m4

Click the Create load button in the side toolbar.

Select the Create point load option from the additional tools displayed. Click at (6 60) to add a point load at the top of the vertical beam.

Proceed to the Mesh tabsheet to generate the mesh.

Mesh generation

• Click the Generate mesh. Keep the Element distribution as Coarse.

• Inspect the generated mesh.

As the geometry has changed, all calculation phases have to be redefined.

1.2.1 PERFORMING CALCULATIONS

Proceed to the Staged construction mode.

Initial conditions

As in the previous example, the K0 procedure will be used to generate the initialconditions.

• All the structural elements should be inactive in the Initial Phase.

• No excavation is performed in the Initial Phase. So, the basement volume should beactive and the material assigned to it should be Lacustrine clay.

Construction stages

Instead of constructing the building in one calculation stage, separate calculation phaseswill be used. In Phase 1, the construction of the walls and the excavation is modelled. InPhase 2, the construction of the floor and beams is modelled. The activation of the loads



is modelled in the last phase (Phase 3).

The calculation type for the phases representing the construction stages is set bydefault to Plastic.

• Rename the Phase_1 to "Excavation".

• Deactivate the soil volume located over the foundation by selecting it and by clickingon the checkbox in front of it in the Selection explorer.

• In the Model explorer click the checkbox in front of the plates corresponding to thebasement walls to activate them.

In the Phases explorer click the Add phase button. A new phase (Phase_2) isadded. Double-click Phase_2. The Phases window pops up.

• Rename the phase by defining its ID as "Construction". Keep the default settings ofthe phase and close the Phases window.

• In the Model explorer click the checkbox in front of the plate corresponding to thebasement floor to activate it.

• In the Model explorer click the checkbox in front of the beams to activate all thebeams in the project.

Add a new phase following the Construction phase. Rename it to "Loading".

• In the Model explorer click the checkbox in front of the Surface loads to activate thesurface load on the basement floor. Set the value of the z−component of the load to−5.3. This indicates a load of 5.3 kN/m2, acting in the negative z−direction.

• In the Model explorer, click the checkbox in front of Line loads to activate the lineloads on the basement walls. Set the value of the z−component of each load to−385. This indicates a load of 385 kN/m, acting in the negative z−direction.

• In the Model explorer click the checkbox in front of Point loads to activate the pointload on the basement column. Set the value of the z−component of the load to−11650. This indicates a load of 11650 kN, acting in the negative z−direction.

Click the Preview phase button to check the settings for each phase.

• As the calculation phases are completely defined, calculate the project. Ignore thewarning that no nodes and stress points have been selected for curves.

• Save the project after the calculation.

Viewing calculation results

• Select Construction option in the Phases explorer.

Click the View calculation results button to open the Output program. The deformedmesh at the end of this phase is shown.

• Select the last phase in the Displayed step drop-down menu to switch to the resultsat the end of the last phase.

In order to evaluate stresses and deformations inside the geometry, select theVertical cross section tool. A top view of the geometry is presented and the Crosssection points window appears. As the largest displacements appear under thecolumn, a cross section here is most interesting.


TUTORIAL MANUAL

• Enter (0.0 6.0) and (75.0 6.0) as the coordinates of the first point (A) and the secondpoint (A') respectively in the Cross section points window.

• Click OK. A vertical cross section is presented. The cross section can be rotated inthe same way as a regular 3D view of the geometry.

• Select Total displacements→ uz from the Deformations menu (Figure 1.19). Themaximum and minimum values of the vertical displacements are shown in thecaption. If the title is not visible, select this option from the View menu.

Figure 1.19 Cross section showing the total vertical displacement

• Press <CTRL><+> and <CTRL><−> to move the cross section.

• Return to the three dimensional view of the geometry by selecting this window fromthe list in the Window menu.

• Double-click the floor. A separate window will appear showing the displacements ofthe floor. To look at the bending moments in the floor, select M11 from the Forcesmenu.

Click the Shadings button. The plot in Figure 1.20 will be displayed.

To view the bending moments in tabulated form, click the Table option in the Toolsmenu. A new window is opened in which a table is presented, showing the values ofbending moments in each node of the floor.



Figure 1.20 Bending moments in the basement floor

1.3 CASE C: PILE-RAFT FOUNDATION

As the displacements of the raft foundation are rather high, embedded piles will be usedto decrease these displacements. These embedded piles represent bored piles with alength of 20 m and a diameter of 1.5 m.

Objectives:

• Using embedded piles.

• Defining material data set for embedded piles.

• Creating multiple copies of entities.

Geometry input

The geometry used in this exercise is the same as the previous one, except for the pilefoundation. It is not necessary to create a new model; you can start from the previousmodel, store it under a different name and modify it. To perform this, follow these steps:

Start the PLAXIS 3D program. The Quick select dialog box will appear in which theproject of Case B should be selected.

• Select the Save project as option in the File menu to save the project under adifferent name (e.g. "Tutorial 1c").

Definition of embedded pile

• Proceed to the Structures mode.

Click the Create line button at the side tool bar and select the Create embedded pilefrom the additional tools that appear.


TUTORIAL MANUAL

• Define a pile from (6 6 -2) to (6 6 -22).

Open the material data base and set the Set type to Embedded piles.

• Create a data set for the embedded pile according to Table 1.4. The value for thecross section area A and the moments of inertia I2, I3 and I23 are automaticallycalculated from the diameter of the massive circular pile. Confirm the input byclicking OK.

Table 1.4 Material properties of embedded pile

Parameter Name Pile foundation Unit

Young's modulus E 3 · 107 kN/m2

Unit weight γ 6.0 kN/m3

Pile type - Predefined −Predefined pile type - Massive circular pile −Diameter Diameter 1.5 mSkin resistance Type Linear −Maximum traction allowed at the top of theembedded pile

Ttop,max 200 kN/m

Maximum traction allowed at the bottom ofthe embedded pile

Tbot ,max 500 kN/m

Base resistance Fmax 1 · 104 kN

• Drag and drop the Pile data to the embedded pile in the draw area. The embeddedpile will change colour to indicate that the material set has been assignedsuccessfully.


Hint: A material set can also be assigned to an embedded pile by right-clicking iteither in the draw area or in the Selection explorer and the Model explorerand selecting the material from the Set material option in the displayed menu.

Click the Select button and select the embedded pile.

Click the Create array button.

• In the Create array window, select the 2D, in xy plane option for shape.

• Keep the number of columns as 2. Set the distance between the columns to x = 12and y = 0.

• Keep the number of rows as 2. Set the distance between the rows to x = 0 andy = 12 (Figure 1.21).

• Press OK to create the array. A total of 2x2 = 4 piles will be created.

Mesh generation

As the geometry model is complete now, the mesh can be generated.

Create the mesh. Keep the Element distribution as Coarse.

View the mesh.

• Click the eye button in front of the Soil subtree in the Model explorer to hide the soil.The embedded piles can be seen (Figure 1.22).



Figure 1.21 Create array window

• Close the mesh preview.

Figure 1.22 Partial geometry of the model in the Output

Performing calculations

After generation of the mesh, all construction stages must be redefined. Even though inpractice the piles will be constructed in another construction stage than construction ofthe walls, for simplicity both actions will be done in the same construction stage in thistutorial. To redefine all construction stages, follow these steps:

• Switch to the Staged construction mode.

• Check if the K0 procedure is selected as Calculation type for the initial phase. Make


TUTORIAL MANUAL

sure that all the structural elements are inactive and all soil volumes are active. Thematerial assigned to it is Lacustrine clay.

• Select the Excavation phase in the Phases explorer.

• Make sure that the basement soil is excavated and the basement walls are active.

• Activate all the embedded piles.

• In the Phases explorer select the Construction phase. Make sure that all thestructural elements are active.

• In the Phases explorer select the Loading phase. Make sure that all the structuralelements and loads are active.

Calculate the project.

• Save the project after the calculation is finished.

• Select the Loading phase and view the calculation results.

• Double-click the basement floor. Select the M11 option from the Forces menu. Theresults are shown in Figure 1.23.

Figure 1.23 Bending moments in the basement floor

• Select the view corresponding to the deformed mesh in the Window menu.

Click the Hide soil button in the side toolbar.

• To view the embedded piles press <Shift> and keep it pressed while clicking on thesoil volume in order to hide it.

Click the Select structures button. To view all the embedded piles, press<Ctrl>+<Shift> keys and double click on one of the piles.

• Select the option N in the Forces menu to view the axial loads in the embeddedpiles. The plot is shown in Figure 1.24.



Figure 1.24 Resulting axial forces (N) in the embedded piles


TUTORIAL MANUAL


EXCAVATION IN SAND

2 EXCAVATION IN SAND

This tutorial describes the construction of an excavation pit in soft clay and sand layers.The pit is a relatively small excavation of 12 by 20 m, excavated to a depth of 6.5 m belowthe surface. Struts, walings and ground anchors are used to prevent the pit to collapse.After the full excavation, an additional surface load is added on one side of the pit.

50.0 m

80.0 m

(30 20) (50 20)

(30 32) (50 32)

Strut

Ground anchors

(34 19) (41 19)

(34 12) (41 12)

4.0 m

4.0 m

4.0 m

5.0 m5.0 m5.0 m5.0 m

Figure 2.1 Top view of the excavation pit

The proposed geometry for this exercise is 80 m wide and 50 m long, as shown in Figure2.1. The excavation pit is placed in the center of the geometry. Figure 2.2 shows a crosssection of the excavation pit with the soil layers. The clay layer is considered to beimpermeable.

Objectives:

• Using the Hardening Soil model

• Modelling of ground anchors

• Using interface features

• Defining over-consolidation ratio (OCR)

• Prestressing a ground anchor

• Changing water conditions

• Selection of stress points to generate stress/strain curves

• Viewing plastic points


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z = 0z = -1

z = -4

z = -9.5

z = -11

z = -20

Fill

Sand

Sand

Soft clay

Sheet pile walls

(62 24 -9)(18 24 -9)

Figure 2.2 Cross section of the excavation pit with the soil layers

2.1 GEOMETRY

To create the geometry model, follow these steps:

Project properties

• Start a new project.

• Enter an appropriate title for the project.

• Define the limits for the soil contour as xmin = 0, xmax = 80, ymin = 0 and ymax = 50.

2.1.1 DEFINITION OF SOIL STRATIGRAPHY

In order to define the soil layers, a borehole needs to be added and material propertiesmust be assigned. As all soil layers are horizontal, only a single borehole is needed.

Create a borehole at (0.0 0.0). The Modify soil layers window pops up.

• Add 4 layers with bottom levels at -1, -9.5, -11, -20. Set the Head in the boreholecolumn to -4 m.

Open the Material sets window.

• Create a new data set under Soil and interfaces set type.

• Identify the new data set as "Fill".

• From the Material model drop-down menu, select Hardening Soil model. In contrastwith the Mohr-Coulomb model, the Hardening Soil model takes into account thedifference in stiffness between virgin-loading and unloading-reloading. For adetailed description of the Hardening Soil model, see the Chapter 6 in the MaterialModels Manual.

• Define the saturated and unsaturated unit weights according to Table 2.1.

• In the Parameters tabsheet, enter values for E ref50 , E ref

oed , E refur , m, c'ref , ϕ'ref , ψ and

ν 'ur according to Table 2.1. Note that Poisson's ratio is an advanced parameter.

• As no consolidation will be considered in this exercise, the permeability of the soilwill not influence the results. Therefore, the default values can be kept in the Flowparameters tabsheet.


EXCAVATION IN SAND

Table 2.1 Material properties for the soil layers

Parameter Name Fill Sand Soft Clay Unit

General

Material model Model Hardening Soilmodel

Hardening Soilmodel

Hardening Soilmodel

−

Drainage type Type Drained Drained Undrained A −Unit weight above phreatic level γunsat 16.0 17.0 16.0 kN/m3

Unit weight below phreatic level γsat 20.0 20.0 17.0 kN/m3

Parameters

Secant stiffness for CD triaxialtest

E ref50 2.2 · 104 4.3 · 104 2.0 · 103 kN/m2

Tangent oedometer stiffness E refoed 2.2 · 104 2.2 · 104 2.0 · 103 kN/m2

Unloading/reloading stiffness E refur 6.6 · 104 1.29 · 105 1.0 · 104 kN/m2

Power for stress leveldependency of stiffness

m 0.5 0.5 1.0 −

Cohesion c'ref 1 1 5 kN/m2

Friction angle ϕ' 30.0 34.0 25.0 ◦

Dilatancy angle ψ 0.0 4.0 0.0 ◦

Poisson's ratio ν 'ur 0.2 0.2 0.2 −Interfaces

Interface strength − Manual Manual Manual −Interface reduction factor Rinter 0.65 0.7 0.5 −Initial

K0 determination − Automatic Automatic Automatic −Lateral earth pressure coefficient K0 0.5000 0.4408 0.7411 −Over-consolidation ratio OCR 1.0 1.0 1.5 −Pre-overburden pressure POP 0.0 0.0 0.0 −

• In the Interfaces tabsheet, select Manual in the Strength box and enter a value of0.65 for the parameter Rinter . This parameter relates the strength of the interfaces tothe strength of the soil, according to the equations:

ci = Rinter csoil and tanϕi = Rinter tanϕi ≤ tanϕsoil

Hence, using the entered Rinter -value gives a reduced interface friction and interfacecohesion (adhesion) compared to the friction angle and the cohesion in the adjacentsoil.

Hint: When the Rigid option is selected in the Strength drop-down, the interfacehas the same strength properties as the soil (Rinter = 1.0).

» Note that a value of Rinter < 1.0, reduces the strength as well as the stiffnessof the interface (Section 6.1.4 of the Reference Manual).

• In the Initial tabsheet, define the OCR-value according to Table 2.1.

• Click OK to close the window.

• In the same way, define the material properties of the "Sand" and "Soft Clay"materials as given by Table 2.1.

• After closing the Material sets window, click the OK button to close the Modify soillayers window.

• In the Soil mode right click on the upper soil layer. In the appearing right hand


TUTORIAL MANUAL

mouse button menu, select the Fill option in the Set material menu.

• In the same way assign the Soft Clay material to the soil layer between y = −9.5 mand y = −11.0 m.

• Assign the Sand material to the remaining two soil layers.

• Proceed to the Structures mode to define the structural elements.

Hint: The Tension cut-off option is activated by default at a value of 0 kN/m2. Thisoption is found in the Advanced options on the Parameters tabsheet of theSoil window. Here the Tension cut-off value can be changed or the optioncan be deactivated entirely.


The creation of sheet pile walls, walings, struts and surface loads and ground anchors isdescribed below.

Create a surface between (30 20 0), (30 32 0), (50 32 0) and (50 20 0).

Extrude the surface to z = −1, z = −6.5 and z = −11.

• Right-click on the deepest created volume (between z = 0 and z = −11) and selectthe Decompose into surfaces option from the appearing menu.

• Delete the top surfaces (2 surfaces). An extra surface is created as the volume isdecomposed.

• Hide the excavation volumes (do not delete). The eye button in the Model explorerand the Selection explorer trees can be used to hide parts of the model and simplifythe view. A hidden project entity is indicated by a closed eye.

Click the Create structure button.

Create beams (walings) around the excavation circumference at level z = −1m.Press the <Shift> key and keep it pressed while moving the mouse cursor in the −zdirection. Stop moving the mouse as the z− coordinate of the mouse cursor is −1in the cursor position indicator. Note that as you release the <Shift> key, the z−coordinate of the cursor location does not change. This is an indication that you candraw only on the xy -plane located at z = −1.

• Click on (30 20 -1), (30 32 -1), (50 32 -1), (50 20 -1), (30 20 -1) to draw the walings.Click on the right mouse button to stop drawing walings.

Create a beam (strut) between (35 20 -1) and (35 32 -1). Press <Esc> to enddefining the strut.

Create data sets for the walings and strut according to Table 2.2 and assign thematerials accordingly.

Copy the strut into a total of three struts at x = 35 (existing), x = 40, and x = 45.


EXCAVATION IN SAND

Table 2.2 Material properties for the beams

Parameter Name Strut Waling Unit

Cross section area A 0.007367 0.008682 m2

Unit weight γ 78.5 78.5 kN/m3

Material behaviour Type Linear Linear −Young's modulus E 2.1 · 108 2.1 · 108 kN/m2

Moment of Inertia I3 5.073 · 10−5 1.045 · 10−4 m4

I2 5.073 · 10−5 3.66 · 10−4 m4

Modelling ground anchors

In PLAXIS 3D ground anchors can be modelled using the Node-to-node anchor and theEmbedded pile options as described in the following:

First the ungrouted part of the anchor is created using the Node-to-node anchorfeature. Start creating a node-to-node anchor by selecting the corresponding buttonin the options displayed as you click on the Create structure button.

• Click on the command line and type "30 24 -1 21 24 -7 " . Press <Enter> and <Esc>to create the ungrouted part of the first ground anchor.

• Create a node-to-node anchor between the points (50 24 -1) and (59 24 -7).

The grouted part of the anchor is created using the Embedded pile option. Createembedded piles between (21 24 -7) and (18 24 -9) and between (59 24 -7) and (6224 -9).

Create a data set for the embedded pile and a data set for the node-to-node anchoraccording to Table 2.3 and Table 2.4 respectively. Assign the data sets to thenode-to-node anchors and to the embedded piles.

Table 2.3 Material properties for the node-to-node anchors

Parameter Name Node-to-node anchor Unit

Material type Type Elastic −Axial stiffness EA 6.5·105 kN

Table 2.4 Material properties for the embedded piles (grout body)

Parameter Name Grout Unit

Young's modulus E 3 · 107 kN/m2

Unit weight γ 24 kN/m3

Pile type − Predefined −Predefined pile type − Massive circular pile −Diameter Diameter 0.14 mSkin friction distribution Type Linear −Skin resistance at the top of theembedded pile

Ttop,max 200 kN/m

Skin resistance at the bottom of theembedded pile

Tbot ,max 0.0 kN/m

Base resistance Fmax 0.0 kN

Hint: The colour indicating the material set assigned to the entities in project canbe changed by clicking on the Colour box of the selected material set andselecting a colour from the Colour part of the window.


TUTORIAL MANUAL

The remaining grouted anchors will be created by copying the defined grouted anchor.

Click on the Select button and click on all the elements composing both of theground anchors keeping the <Ctrl> key pressed.

Use the Create array function to copy both ground anchors (2 embedded piles + 2node-to-node anchors) into a total of 4 complete ground anchors located at y = 24and y = 28 by selection the 1D, in y direction option in the Shape drop-down menuand define the Distance between columns as 4 m.

Multi-select all parts of the ground anchors (8 entities in total). While all parts areselected and the <Ctrl> key is pressed, click the right mouse button and select theGroup from the appearing menu.

In the Model explorer tree, expand the Groups subtree by clicking on the (+) in frontof the groups.

• Click the Group_1 and rename it to "GroundAnchors".

Hint: The name of the entities in the project should not contain any space orspecial character except "_" .

To define the sheet pile walls and the corresponding interfaces, follow these steps:

Select all four vertical surfaces created as the volume was decomposed. Keepingthe <Ctrl> key pressed, click the right mouse button and select the Create plateoption from the appearing menu.

Create a data set for the sheet pile walls (plates) according to Table 2.5. Assign thedata sets to the four walls.

• As all the surfaces are selected, assign both positive and negative interfaces tothem using the options in the right mouse button menu.

Hint: The term 'positive' or 'negative' for interfaces has no physical meaning. Itonly enables distinguishing between interfaces at each side of a surface.

Table 2.5 Material properties of the sheet pile walls

Parameter Name Sheet pile wall Unit

Thickness d 0.379 mWeight γ 2.55 kN/m3

Type of behaviour Type Linear, non-isotropic −Young's modulus E1 1.46 · 107 kN/m2

E2 7.3 · 105 kN/m2

Poisson's ratio ν 0.0 −Shear modulus G12 7.3 · 105 kN/m2

G13 1.27 · 106 kN/m2

G23 3.82 · 105 kN/m2

Non-isotropic (different stiffnesses in two directions) sheet pile walls are defined. Thelocal axis should point in the correct direction (which defines which is the 'stiff' or the 'soft'direction). As the vertical direction is generally the stiffest direction in sheet pile walls,


EXCAVATION IN SAND

local axis 1 shall point in the z−direction.

In the Model explorer tree expand the Surfaces subtree, set AxisFunction to Manualand set Axis1z to −1. Do this for all the pile wall surfaces.

Create a surface load defined by the points: (34 19 0), (41 19 0), (41 12 0), (34 120). The geometry is now completely defined.

Hint: The first local axis is indicated by a red arrow, the second local axis isindicated by a green arrow and the third axis is indicated by a blue arrow.More information related to the local axes of plates is given in the ReferenceManual.

2.2 MESH GENERATION

• Proceed to the Mesh mode.

Create the mesh. Set the Element distribution to Coarse.

View the mesh. Hide the soil in the model to view the embedded piles.

2.3 PERFORMING CALCULATIONS

The calculation consists of 6 phases. The initial phase consists of the generation of theinitial stresses using the K0 procedure. The next phase consists of the installation of thesheet piles and a first excavation. Then the walings and struts will be installed. In phase3, the ground anchors will be activated and prestressed. Further excavation will beperformed in the phase after that. The last phase will be the application of the additionalload next to the pit.

• Click on the Staged construction tab to proceed with definition of the calculationphases.

• The initial phase has already been introduced. Keep its calculation type as K0procedure. Make sure all the soil volumes are active and all the structural elementsare inactive.

Add a new phase (Phase_1). The default values of the parameters will be used forthis calculation phase.

• Deactivate the first excavation volume (from z = 0 to z = −1).

• In the Model explorer, activate all plates and interfaces by clicking on the checkboxin front of them. The active elements in the project are indicated by a green checkmark in the Model explorer.

Add a new phase (Phase_2). The default values of the parameters will be used forthis calculation phase.

• In the Model explorer activate all the beams.

Add a new phase (Phase_3). The default values of the parameters will be used for


TUTORIAL MANUAL

this calculation phase.

• In the Model explorer activate the GroundAnchors group.

Select one of the node-to-node anchors.

In the Selection explorer expand the node-to node anchor features.

• Click Adjust prestress and change this into True. Enter a prestress force of 200 kN(Figure 2.3).

• Do the same for all the other node-to-node anchors.

Figure 2.3 Node-to-node anchor in the Selection explorer

Add another phase (Phase_4). The default values of the parameters will be used forthis calculation phase.

• Proceed to the Water levels mode.

Select the soil volume to be excavated in this phase (between z = −1 andz = −6.5).

In the Selection explorer expand the soil entity and subsequently expand theWaterConditions feature. Click on the Conditions and select the Dry option from thedrop-down menu.

Figure 2.4 Water conditions in the Selection explorer

• Hide the soil around the excavation.

Select the soil volume below the excavation (between z = −6.5 and z = −9.5).

In Selection explorer expand the soil entity and subsequently expand theWaterConditions feature.

• Click Conditions and select Head from the drop-down menu. Enter zref = −6.5 m.

Select the soft clay volume below the excavation.


EXCAVATION IN SAND

• Set the water conditions to Interpolate.

• Proceed to Staged construction mode.

• Deactivate the volume to be excavated (between z = −1 and z = −6.5).

Preview this calculation phase.

Click the Vertical cross section button in the Preview window and define the crosssection by drawing a line across the excavation.

• Select the psteady option from the Stresses menu.

Display the contour lines for steady pore pressure distribution. Make sure that theLegend option is checked in View menu. The steady state pore pressure distributionis displayed in Figure 2.5. Scroll the wheel button of the mouse to zoom in or out toget a better view.

Figure 2.5 Preview of the steady state pore pressures in Phase_4 in a cross section

• Click on the Close button to return to the Input program.

Add another phase (Phase_5). The default values of the parameters will be used forthis calculation phase.

• Activate the surface load and set σz = −20kN/m2.

Defining points for curves

Before starting the calculation process, some stress points next to the excavation pit andloading are selected to plot a stress strain curve later on.

Click the Select points for curves button. The model and Select points window willbe displayed in the Output program.

• Define (37.5 19 -1.5) as Point-of-interest coordinates.

• Click the Search closest button. The number of the closest node and stress pointwill be displayed.

• Click the checkbox in front of the stress point to be selected. The selected stresspoint will be shown in the list.

• Select also stress points near the coordinates (37.5 19 -5), (37.5 19 -6) and (37.5 19-7) and close the Select points window.


TUTORIAL MANUAL

• Click the Update button to close the Output program.

Start the calculation process.

Save the project when the calculation is finished.

Hint: Instead of selecting nodes or stress points for curves before starting thecalculation, points can also be selected after the calculation when viewingthe output results. However, the curves will be less accurate since only theresults of the saved calculation steps will be considered.

» To plot curves of structural forces, nodes can only be selected after thecalculation.

» Nodes or stress points can be selected by just clicking them. When movingthe mouse, the exact coordinates of the position are given in the cursorlocation indicator bar at the bottom of the window.

2.4 VIEWING THE RESULTS

After the calculations, the results of the excavation can be viewed by selecting acalculation phase from the Phases tree and pressing the View calculation results button.

Select the final calculation phase (Phase_5) and click the View calculation resultsbutton. The Output program will open and will show the deformed mesh at the endof the last phase.

• The stresses, deformations and three dimensional geometry can be viewed byselecting the desired output from the corresponding menus. For example, choosePlastic points from the Stresses menu to investigate the plastic points in the model.

• In the Plastic points window, Figure 2.6, select all the options except the Elasticpoints and the Show only inaccurate points options. Figure 2.7 shows the plasticpoints generated in the model at the end of the final calculation phase.

Figure 2.6 Plastic points window

Start selecting structures. Click at a part of the wall to select it. Press <Ctrl + A>simultaneously on the keyboard to select all wall elements. The selected wallelements will colour red.


EXCAVATION IN SAND

Figure 2.7 Plastic points at the end of the final phase

• While holding the <Ctrl> key or <Shift> key on the keyboard, double click at one ofthe wall elements to see the deformations plane of the total displacements |u| in allwall elements.

To generate a curve, select the Curves manager option from the Tools menu or clickthe corresponding button in the toolbar.

• All pre-selected stress points are shown in the Curve points tabsheet of the Curvesmanager window.

• Create a new chart.

• Select point K from the drop-down menu for x−axis of the graph. Select ε1 underTotal strains.

• Select point K from the drop-down menu for y−axis of the graph. Select σ'1 underPrincipal effective stresses (Figure 2.8).

• Invert the sign of both axis by checking the corresponding boxes.

• Click OK to confirm the input.

The graph will now show the major principal strain against the major principal stress.Both values are zero at the beginning of the initial conditions. After generation of theinitial conditions, the principal strain is still zero whereas the principal stress is not zeroanymore. To plot the curves of all selected stress points in one graph, follow these steps:

• Select Add curve→ From current project from right mouse button menu.

• Generate curves for point L, M and N in the same way.

The graph will now show the stress-strain curves of all four stress points (Figure 2.9). Tosee information about the markers, make sure the Value indication option is selectedfrom the View menu and hold the mouse on a marker for a while. Information about thecoordinates in the graph, the number of the point in the graph, the number of the phaseand the number of the step is given. Especially the lower stress points show aconsiderable increase in the stress when the load is applied in the last phase.


TUTORIAL MANUAL

Figure 2.8 Curve generation window

Figure 2.9 Stress - Strain curve

Hint: To re-enter the Curve generation window (in the case of a mistake, a desiredregeneration or a modification), the Curve settings option from the Formatmenu can be selected. As a result the Curves settings window appears, onwhich the Regenerate button should be clicked.

» The Chart settings option in the Format menu may be used to modify thesettings of the chart.

To create a stress path plot for stress point K follow these steps:

• Create a new chart.

• In the Curves generation window, select point K from the drop-down menu of thex−axis of the graph and σ'yy under Cartesian effective stresses.


EXCAVATION IN SAND

• Select point K from the drop-down menu of the y−axis of the graph. Select σ'zzunder Cartesian effective stresses.

• Click OK to confirm the input (Figure 2.10).

Figure 2.10 Vertical effective stress (σ'zz ) versus horizontal effective stress (σ'yy ) at stress point Klocated near (37.5 19 -1.5)


TUTORIAL MANUAL


LOADING OF A SUCTION PILE

3 LOADING OF A SUCTION PILE

In this tutorial a suction pile in an off-shore foundation will be considered. A suction pile isa hollow steel pile with a large diameter and a closed top, which is installed in the seabedby pumping water from the inside. The resulting pressure difference between the outsideand the inside is the driving force behind this installation.

In this exercise, the length of the suction pile is 10 m and the diameter is 4.5 m. Ananchor line is attached on the side of the pile, 7 m from the top. To avoid local failure ofthe pile, the thickness of the tube where the anchor line acts on the pile is increased. Thesoil consists of silty sand. To model undrained behaviour, an undrained stress analysiswith undrained strength parameters will be performed (Section 6.2 of the ReferenceManual). This exercise will investigate the displacement of the suction pile under workingload. Four different angles of the working load will be considered. The installationprocess itself will not be modelled. The geometry for the problem is sketched in Figure3.1.

Objectives:

• Importing volumes

• Undrained effective stress analysis with undrained strength parameters

• Soil cohesion increases with depth

• Copying material data sets

• Changing settings in Output

• Selecting a node after calculation to generate a curve with structural forces

z = -6.5 mz = -7.0 m

z = -7.5 m

z = -10 m

z

x

4.5 m

α

Figure 3.1 Geometry of the suction pile

3.1 GEOMETRY

An area of 60 m wide and 60 m long surrounding the suction pile will be modelled. Withthese dimensions the model is sufficiently large to avoid any influence from the modelboundaries.


TUTORIAL MANUAL

Project properties

To define the geometry for this exercise, follow these steps:

• Start the Input program and select New project from the Create/Open project dialogbox.

• Enter an appropriate title for the exercise.

• Keep the standard units and set the model dimensions to xmin = −30 m, xmax = 30m, ymin = −30 m, ymax = 30 m.

• Click OK.


In the current example only one horizontal soil layer is present. A single borehole issufficient to define it.

Add a borehole to the geometry.

• In the Modify soil layers window add a soil layer with top boundary at z = 0 m andbottom boundary at z = −30 m.

• The Head value is 50.0 m, which means 50 m depth above the soil.

Open the Material sets window and create the data sets given in Table 3.1. In theParameters tabsheet deselect the Tension cut-off option in the advancedparameters for strength. In this exercise, the permeability of the soil will notinfluence the results. Instead of using effective strength properties, the cohesionparameter will be used in this example to model undrained shear strength.Advanced parameters can be entered after expanding the Advanced data tree in theParameters tabsheet.

Hint: The Interface data set can be quickly created by copying the 'Sand' data setand changing the Rinter value.

• Assign the 'Sand' material data set to the soil layer and close the Material setswindow.


The suction pile is modelled in the Structures mode using predefined volumes. To modela suction pile:

Import the standard cylinder. The standard cylinder is saved in the<example_cylinder_vertical_D1h1_centered.3ds> file in the Importables folder of theinstallation directory of PLAXIS 3D. The imported volume is edited in the Importstructure volumes window. Import solid is a PLAXIS VIP feature.

• Modify the scale such that the diameter is 4.5 m and the height is 10 m.



Table 3.1 Material properties of the sand layer and its interface

Parameter Name Sand Interface Unit

General

Material model Model Mohr-Coulomb Mohr-Coulomb −Drainage type Type Undrained B Undrained B −Soil weight γunsat , γsat 20 20 kN/m3

Parameters

Young's modulus E ' 1000 1000 kN/m2

Poisson's ratio ν ' 0.35 0.35 −Shear strength su,ref 1.0 1.0 kN/m2

Friction angle ϕu 0.0 0.0 ◦

Dilatancy angle ψ 0.0 0.0 ◦

Increase in stiffness E 'inc 1000 1000 kN/m2/mReference level zref 0.0 0.0 mIncrease in cohesion su,inc 4.0 4.0 kN/m2/mReference level zref 0.0 0.0 m

Interfaces

Interface strength − Manual Rigid −Interface strength reduction Rinter 0.7 1.0 −Initial

K0 determination − Manual Manual −Lateral earth pressure coeff. K0,x , K0,y 0.5 0.5 −

• Define the coordinates of the insertion point such that the top of the anchor is at thesea bottom level (z = 0) and the bottom of the anchor is at z = −10 (Figure 3.2).

Figure 3.2 Import structure volumes window

• Decompose the imported volume into surfaces by right-clicking it and selecting theDecompose into surfaces option from the appearing menu.


TUTORIAL MANUAL

Hint: As an alternative for the import of a cylinder, the corresponding cylindercommand can be used to create the suction pile. Information about thecommands available in the program is displayed when the Commandreference option is selected in the Help menu.

• Make the cylinder mantle into a plate, positive interface and negative interface byright-clicking on it and selecting the corresponding options from the appearing menu.

Open the material data base. Select Plates as set type. Create three data setsaccording to the information in Table 3.2.

Table 3.2 Material properties for the suction pile

Parameter Name Thin wall Thick wall Top Unit

Thickness d 0.05 0.15 0.05 mWeight γ 58.5 58.5 68.5 kN/m3

Type ofbehaviour

Type Linear, isotropic Linear, isotropic Linear, isotropic −

Young'smodulus

E 2.1 · 108 2.1 · 108 2.1 · 108 kN/m2

Poisson'sratio

ν 0.1 0.1 0.1 −

Shearmodulus

G 9.545 · 107 9.545 · 107 9.545 · 107 kN/m2

• Assign Thin wall to the anchor tube and close the Material data set window.

• Hide the anchor tube and the original volume object using the Hide option in theright mouse button menu. Note that the top and the bottom surfaces are visible.

Select the top surface and click on the Create array button in the side tool bar.Select the 1D, in z direction option for Shape. Keep the number of columns as 2 anddefine z as −6.5 for the Distance between columns.

• Repeat the previous step to create surfaces at z = −7.0 and z = −7.5.

• Make the top surface into a plate. Assign Top material data set to it.

• Assign a positive interface to the bottom surface (z= -10 m). Assign the 'Interface'data set to the bottom interface.

• Right-click on the surface located at z = −7.0 m and select the Decompose intooutlines option from the appearing menu.

• Right-click on the point near (2.25 0.0 -7.0) and select the Create point load optionfrom the appearing menu. The actual load values will be assigned when thecalculation phases are defined.

The geometry of the project is defined.

3.2 MESH GENERATION

In order to generate the mesh:

• The mesh is automatically refined near the plates and load. Select the point load byclicking on it in the model. In the Selection explorer note that the Fineness factor



value is 0.5 and it is displayed in a lighter shade of green in the model.

Generate the mesh. Set the element distribution to Coarse.

• Proceed to the Staged construction mode.


The calculation for this exercise will consist of 6 phases. These are the determination ofinitial conditions, the installation of the suction pile and four different load conditions. Theeffect of the change of the load direction while keeping the magnitude unchanged will beanalysed.

• Click on the Staged construction tab to proceed with the definition of the calculationphases. Keep the calculation type of the Initial phase to K0 procedure. Ensure thatall the structures and interfaces are switched off.

Add a new calculation phase and rename it as 'Install pile'.

• Activate all the plates and interfaces in the project. Assign the Thick wall material tothe plate sections just above and just below the point load. It may be necessary tohide (NOT deactivate) the positive interface around the anchor. Load is not active.

Add a new phase and rename it as 'Load pile 30 degrees'. Open the Phaseswindow and check the Reset displacements to zero checkbox in the Deformationcontrol parameters subtree.

• Activate the point load and set Fx = 3897 kN, Fz = 2250 kN.

• Define the remaining phases according to the information in Table 3.3. For eachphase the Reset displacements to zero option is to be selected.

• Calculate and save the project.

Table 3.3 Load informationPhase Reference phase Fx Fz

Load pile 30 degrees [Phase_2] Phase_1 3897 kN 2250 kN




The order of the phases is indicated in the Phases explorer (Figure 3.3). Calculation ofPhase_1 starts after the calculation of Initial phase is completed. The calculation of theremaining phases starts after the calculation of the pile installation phase is completed.



TUTORIAL MANUAL


To view the results:

• View the results of the last calculation phase. The deformed mes of the wholegeometry will be shown. In particular, the displacements of the suction pile itself areof interest.

• To make the suction pile visible deselect the Soil and the Interfaces option in Modelexplorer.

Click on the Select structures button and select the pile wall. This will select only apart of the wall. Press <Ctrl + A> to select all the wall elements of the suction pile.

• Keeping the <Ctrl> key pressed, double click the pile walls. The results for the wallof the suction pile are displayed in a new window.

Select the shadings representation and rotate the model such that the x−axis isperpendicular to the screen.

• If the axes are not visible, select this option from the View menu. It is quite clear thatthe point force acting on the pile does not disturb the displacement field locallyindicating that the pile is sufficiently thick here.

• In the same manner, the total displacements of the suction pile under a differentdirection of the load can be inspected by selecting the appropriate phase from thedrop-down menu. In particular, <Phase_2> is of interest, as in this phase thehorizontal part of the load will have the largest value (Figure 3.4).

Figure 3.4 Total displacement of the suction pile at the end of Phase_2


CONSTRUCTION OF A ROAD EMBANKMENT

4 CONSTRUCTION OF A ROAD EMBANKMENT

The construction of an embankment on soft soil with a high groundwater level leads to anincrease in pore pressure. As a result of this undrained behaviour, the effective stressremains low and intermediate consolidation periods have to be adopted in order toconstruct the embankment safely. During consolidation the excess pore pressuresdissipate so that the soil can obtain the necessary shear strength to continue theconstruction process.

This tutorial concerns the construction of a road embankment in which the mechanismdescribed above is analysed in detail. In the analysis two new calculation options areintroduced, namely a consolidation analysis and the calculation of a safety factor bymeans of a safety analysis (phi/c-reduction). It also involves the modelling of drains tospeed up the consolidation process.

12 m12 m 16 m

4 m

3 m

3 m

road embankment

peat

clay

dense sand

Figure 4.1 Situation of a road embankment on soft soil

Objectives:

• Modelling drains

• Consolidation analysis

• Change of permeability during consolidation

• Safety analysis (phi-c reduction)

4.1 GEOMETRY

Figure 4.1 shows a cross section of a road embankment. The embankment is 16 m wide.The slopes have an inclination of 1: 3. The problem is symmetric, so only one half ismodelled (in this case the right half is chosen). A representative section of 2 m isconsidered in the project. The embankment itself is composed of loose sandy soil. Thesubsoil consists of 6 m of soft soil. The upper 3 m of this soft soil layer is modelled as apeat layer and the lower 3 m as clay. The phreatic level is located 1 m below the originalground surface. Under the soft soil layers there is a dense sand layer of which 4 m areconsidered in the model.

• Start the Input program and select Start a new project from the Quick select dialogbox.

• In the Project tabsheet of the Project properties window, enter an appropriate title.

• Keep the default units and set the model dimensions to xmin = 0, xmax = 60, ymin = 0and ymax = 2.


TUTORIAL MANUAL


The soil layers comprising the embankment foundation are defined using a borehole. Theembankment layers are defined in the Structures mode.

Create a borehole at (0 0). The Modify soil layers window pops up.

• Define three soil layers as shown in Figure 4.2.

• The water level is located at z = -1 m. In the borehole column specify a value of -1 toHead.


• Create soil material data sets according to Table 4.1 and assign them to thecorresponding layers in the borehole (Figure 4.2).

• Close the Modify soil layers window and proceed to the Structures mode to definethe structural elements.

Figure 4.2 Soil layer distribution

Hint: The initial void ratio (einit ) and the change in permeability (ck ) should bedefined to enable the modelling of a change in the permeability due tocompression of the soil. This option is recommended when using advancedmodels.



Table 4.1 Material properties of the road embankment and subsoil

Parameter Name Embankment Sand Peat Clay Unit

General

Material model Model Hardening soil Hardening soil Soft soil Soft soil -

Drainage type Type Drained Drained Undr. (A) Undr. (A) -

Soil unit weight abovephreatic level

γunsat 16 17 8 15 kN/m3

Soil unit weight belowphreatic level

γsat 19 20 12 18 kN/m3

Initial void ratio einit 0.5 0.5 2.0 1.0 -

Parameters

Secant stiffness instandard drainedtriaxial test

E ref50 2.5· 104 3.5· 104 - - kN/m2

Tangent stiffness forprimary oedometerloading

E refoed 2.5· 104 3.5· 104 - - kN/m2

Unloading / reloadingstiffness

E refur 7.5· 104 1.05· 105 - - kN/m2

Power for stress-leveldependency of stiffness

m 0.5 0.5 - - -

Modified compressionindex

λ∗ - - 0.15 0.05 -

Modified swelling index κ∗ - - 0.03 0.01 -

Cohesion cref ' 1.0 0.0 2.0 1.0 kN/m2

Friction angle ϕ' 30.0 33.0 23.0 25.0 ◦

Dilatancy angle ψ 0.0 3.0 0.0 0.0 ◦

Advanced: Set todefault

- Yes Yes Yes Yes -

Flow parameters

Data set - USDA USDA USDA USDA -

Model - VanGenuchten

VanGenuchten

VanGenuchten

VanGenuchten

-

Soil type - Loamy sand Sand Clay Clay -

< 2µm - 6.0 4.0 70.0 70.0 %2µm − 50µm - 11.0 4.0 13.0 13.0 %50µm − 2mm - 83.0 92.0 17.0 17.0 %Set to default - Yes Yes No Yes -

Horizontal permeability(x-direction)

kx 3.499 7.128 0.1 0.04752 m/day

Horizontal permeability(y-direction)

ky 3.499 7.128 0.1 0.04752 m/day

Vertical permeability kz 3.499 7.128 0.02 0.04752 m/day

Change in permeability ck 1· 1015 1· 1015 1.0 0.2 -

Interfaces

Interface strength − Rigid Rigid Rigid Rigid -

Strength reductionfactor

Rinter 1.0 1.0 1.0 1.0 -

Initial

K0 determination − Automatic Automatic Automatic Automatic -

Over-consolidation ratio OCR 1.0 1.0 1.0 1.0 -

Pre-overburdenpressure

POP 0.0 0.0 5.0 0.0 kN/m2


TUTORIAL MANUAL

4.1.2 DEFINITION OF EMBANKMENT AND DRAINS

The embankment and the drains are defined in the Structures mode. To define theembankment layers:

Reorientate the model such that the front view is displayed by clicking thecorresponding button in the toolbar.

Create a surface by defining points at (0 0 0), (0 0 4), (8 0 4) and (20 0 0).

Create a line passing through (0 0 2) and (14 0 2) to define the embankment layers.

Select both the created line and surface by keeping the <Ctrl> key pressed whileclicking them in the model.

Click the Extrude object button.

• Assign a value of 2 to the y-component of the extrusion vector as shown in Figure4.3 and click Apply.

Figure 4.3 Extrusion window

• Delete the surface and the line created before the extrusion.

• Right-click the volume created by extrusion and point to the Soil_4 option in theappearing menu.

• A new menu is displayed. Point to the Set material option and select Embankment.

In this project the effect of the drains on the consolidation time will be investigated bycomparing the results with a case without drains. Drains will only be active for thecalculation phases in the case with drains.

Drains are arranged in a square pattern, having a distance of 2 m between twoconsecutive drains in a row (or column). Only one row of drains will be considered in thistutorial. To create the drain pattern:

Click the Create hydraulic conditions button in the side toolbar.

Click the Create line drain button in the appearing menu. Define a line drain in themodel between points (1 1 0) and (1 1 -6).

Click the Create array button to define the drain pattern.

• In the Create array window select the 1D, in x direction in the Shape drop-downmenu and specify the pattern as shown in Figure 4.4.



Figure 4.4 Settings of the drain pattern

The model geometry is shown in Figure 4.5.

Figure 4.5 Model geometry

4.2 MESH GENERATION


Click the Generate mesh button. Set the element distribution to Coarse.

View the generated mesh. The resulting mesh is shown in Figure 4.6.


TUTORIAL MANUAL

Figure 4.6 The generated mesh


The embankment construction process will be considered twice. In the first calculationthe drains will not be considered.

Initial phase

In the initial situation the embankment is not present. Therefore, the corresponding soilvolumes are deactivated in the initial phase. The K0 procedure can be used to calculatethe initial stresses. The initial water pressures are fully hydrostatic and based on ageneral phreatic level defined by the Head value assigned to the boreholes. For the Initialphase, the Phreatic option is selected for the pore pressure calculation type and theGlobal water level is set to BoreholeWaterlevel_1 corresponding to the water leveldefined by the heads specified for the boreholes.

The boundary conditions for flow can be specified in the Model conditions subtree in theModel explorer. In the current situation the left vertical boundary (Xmin) must be closedbecause of symmetry, so horizontal flow should not occur. The bottom is open becausethe excess pore pressures can freely flow into the deep and permeable sand layer. Theupper boundary is obviously open as well. The view of the GroundwaterFlow subtreeafter the definition is given in Figure 4.7.

Figure 4.7 Boundary conditions for groundwater flow



4.3.1 CONSOLIDATION ANALYSIS

A consolidation analysis introduces the dimension of time in the calculations. In order tocorrectly perform a consolidation analysis a proper time step must be selected. The useof time steps that are smaller than a critical minimum value can result in stressoscillations. The consolidation option in PLAXIS allows for a fully automatic time steppingprocedure that takes this critical time step into account. Within this procedure there arethree main possibilities for the Loading type parameter:

1. Consolidate for a predefined period, including the effects of changes to the activegeometry (Staged construction).

2. Consolidate until all excess pore pressures in the geometry have reduced to apredefined minimum value (Minimum pore pressure).

3. Consolidate until the soil has reached a specified degree of consolidation (Degree ofconsolidation).

Consolidation process - No drains

The embankment construction is divided into two phases. After the first constructionphase a consolidation period of 30 days is introduced to allow the excess pore pressuresto dissipate. After the second construction phase another consolidation period isintroduced from which the final settlements may be determined. Hence, a total of fourcalculation phases have to be defined besides the initial phase.

To define the calculation phases, follow these steps:

Phase 1:

Click the Add phase button to introduce the first construction phase.

In the General subtree select the Consolidation option in the Calculation typedrop-down menu.

The Loading type is by default set to Staged construction. This option will be usedfor this phase.

The Phreatic option is automatically selected for the pore pressure calculation type.Note that the global water level for a calculation phase can be defined in the Watersubtree available under the Model conditions in the Model explorer.

• Specify a value of 2 days to the Time interval and click OK to close the Phaseswindow.

• In the Staged construction mode activate the first part of the embankment.

Click the Add phase button to introduce the next calculation phase.

Phase 2: The second phase is also a Consolidation analysis. In this phase no changesto the geometry are made as only a consolidation analysis to ultimate time is required.

Define the calculation type as Consolidation.

• Specify a value of 30 days to the Time interval. The default values of the otherparameters are used for this phase.



TUTORIAL MANUAL

Phase 3:


• Specify a value of 1 day to the Time interval. The default values of the otherparameters are used.

• In the Staged construction mode activate the second part of the embankment.


Phase 4: The fourth phase is a Consolidation analysis to a minimum pore pressure.


Select the Minimum pore pressure option in the Loading type drop-down menu. Thedefault value for the minimum pressure (|P-stop| = 1.0 kN/m2) as well as the defaultvalues for other parameters are used.

The definition of the calculation phases is complete.

Before starting the calculation, click the Select points for curves button and selectthe following points: As Point A, select the toe of the embankment. The secondpoint (Point B) will be used to plot the development (and decay) of excess porepressures. To this end, a point somewhere in the middle of the soft soil layers isneeded, close to (but not actually on) the left boundary.

Start the calculation.

During a consolidation analysis the development of time can be viewed in the upper partof the calculation info window (Figure 4.8). In addition to the multipliers, a parameterPmax occurs, which indicates the current maximum excess pore pressure. Thisparameter is of interest in the case of a Minimum pore pressure consolidation analysis,where all pore pressures are specified to reduce below a predefined value.

Figure 4.8 Calculation progress displayed in the Active tasks window




After the calculation has finished, select the third phase and click the Viewcalculation results button. The Output window now shows the deformed mesh after

the undrained construction of the final part of the embankment (Figure 4.9). Consideringthe results of the third phase, the deformed mesh shows the uplift of the embankment toeand hinterland due to the undrained behaviour.

Figure 4.9 Deformed mesh after undrained construction of embankment (Phase 3, true scale)

• In the Deformations menu select the Incremental displacements→ |∆u|.Select the Arrows option in the View menu or click the corresponding button in thetoolbar to display the results arrows.

On evaluating the total displacement increments, it can be seen that a failure mechanismis developing (Figure 4.10).

Figure 4.10 Displacement increments after undrained construction of embankment

• Click <Ctrl> + <7> to display the developed excess pore pressures (see Appendix Cof Reference Manual for more shortcuts). They can be displayed by selecting thecorresponding option in the side menu displayed as the Pore pressures option isselected in the Stresses menu.

Click the Center principal directions. The principal directions of excess pressuresare displayed at the center of each soil element. The results are displayed in Figure4.11. It is clear that the highest excess pore pressure occurs under the embankmentcentre.

• Select Phase 4 in the drop down menu.


TUTORIAL MANUAL

Figure 4.11 Excess pore pressures after undrained construction of embankment

Define a vertical cross section passing through (0 1) and (60 1).

Click the Contour lines button in the toolbar to display the results as contours.

• In the View menu select the Viewpoint option. The corresponding window pops up.

• In the Viewpoint window select the Front view option as shown in Figure 4.12.

Figure 4.12 Viewpoint window

Use the Draw scanline button or the corresponding option in the View menu todefine the position of the contour line labels.

Figure 4.13 Excess pore pressure contours after consolidation to Pexcess < 1.0 kN/m2

It can be seen that the settlement of the original soil surface and the embankmentincreases considerably during the fourth phase. This is due to the dissipation of theexcess pore pressures (= consolidation), which causes further settlement of the soil.Figure 4.13 shows the remaining excess pore pressure distribution after consolidation.Check that the maximum value is below 1.0 kN/m2.



The Curves manager can be used to view the development, with time, of the excess porepressure under the embankment. In order to create such a curve, follow these steps:

Click the Curves manager button in the toolbar. The corresponding window pops up.

• In the Charts tabsheet click New. The Curve generation window pops up

• For the x-axis, select the Project option from the drop-down menu and select Timein the tree.

• For the y -axis select the point in the middle of the soft soil layers (Point B) from thedrop-down menu. In the tree select Stresses→ Pore pressure→ pexcess.

• Select the Invert sign option for y-axis.

• Click the Ok to generate the curve.

Click the Settings button in the toolbar. The Settings window will appear displayingthe tabsheet of the created curve.

• Click the Phases button and select the phases 1 to 4 in the appearing window.

• Rename the curve by typing 'Phases 1 - 4' in the Curve title cell.

• Click Apply to update the plot.

Save the chart.

Hint: To display the legend inside the chart area right-click on the name of thechart, point to the View option and select the Legend in chart option in theappearing menu.

Figure 4.14 Development of excess pore pressure under the embankment

Figure 4.14 clearly shows the four calculation phases. During the construction phasesthe excess pore pressure increases with a small increase in time while during theconsolidation periods the excess pore pressure decreases with time. In fact,consolidation already occurs during construction of the embankment, as this involves asmall time interval.


TUTORIAL MANUAL

4.5 SAFETY ANALYSIS

In the design of an embankment it is important to consider not only the final stability, butalso the stability during the construction. It is clear from the output results that a failuremechanism starts to develop after the second construction phase.

It is interesting to evaluate a global safety factor at this stage of the problem, and also forother stages of construction.

In structural engineering, the safety factor is usually defined as the ratio of the collapseload to the working load. For soil structures, however, this definition is not always useful.For embankments, for example, most of the loading is caused by soil weight and anincrease in soil weight would not necessarily lead to collapse. Indeed, a slope of purelyfrictional soil will not fail in a test in which the self weight of the soil is increased (like in acentrifuge test). A more appropriate definition of the factor of safety is therefore:

Safety factor = Smaximum available

Sneeded for equilibrium(4.1)

Where S represents the shear strength. The ratio of the true strength to the computedminimum strength required for equilibrium is the safety factor that is conventionally usedin soil mechanics. By introducing the standard Coulomb condition, the safety factor isobtained:

Safety factor =c − σn tanϕ

cr −σn tanϕr(4.2)

Where c and ϕ are the input strength parameters and σn is the actual normal stresscomponent. The parameters cr and ϕr are reduced strength parameters that are justlarge enough to maintain equilibrium. The principle described above is the basis of aSafety analysis that can be used in PLAXIS to calculate a global safety factor. In thisapproach the cohesion and the tangent of the friction angle are reduced in the sameproportion:

ccr

=tanϕtanϕr

= ΣMsf (4.3)

The reduction of strength parameters is controlled by the total multiplier ΣMsf . Thisparameter is increased in a step-by-step procedure until failure occurs. The safety factoris then defined as the value of ΣMsf at failure, provided that at failure a more or lessconstant value is obtained for a number of successive load steps.

The Safety calculation option is available in the Calculation type drop-down menu in thePhases window.

To calculate the global safety factor for the road embankment at different stages ofconstruction, follow these steps:

• We first want to calculate the safety factor after the first construction stage. In theCalculations program introduce a new calculation phase (Phase_5) and selectPhase 1 in the Start from phase drop-down menu.

In the General subtree, select Safety as calculation type.

The Loading type is automatically changed to Incremental multipliers. This is theonly option available for the Safety calculation type.

• The first increment of the multiplier that controls the strength reduction process, Msf,



is set automatically to 0.1. This value will be used in this tutorial.

Note that the Use pressures from the previous phase option in the Pore pressurecalculation type drop-down menu is automatically selected and grayed out indicatingthat this option cannot be changed

• In order to exclude existing deformations from the resulting failure mechanism,select the Reset displacements to zero option in the Deformation control parameterssubtree. The default values of all the remaining parameters will be used. The firstsafety calculation has now been defined.

• Follow the same steps to create new calculation phases that analyse the stability atthe end of each consolidation phase. In addition to selecting Safety as calculationtype, select the corresponding consolidation phase as the Start from phaseparameter. The Phases explorer displaying the Safety calculation phases is shownin Figure 4.15.

Calculate the safety phases.

Hint: The default value of Max steps in a Safety calculation is 100. In contrast toan Staged construction calculation, the number of additional steps is alwaysfully executed. In most Safety calculations, 100 steps are sufficient to arriveat a state of failure. If not, the number of steps can be increased to amaximum of 10000.

» For most Safety analyses Msf = 0.1 is an adequate first step to start up theprocess. During the calculation process, the development of the totalmultiplier for the strength reduction, ΣMsf , is automatically controlled by theload advancement procedure.

Figure 4.15 Phases explorer displaying the Safety calculation phases

4.5.1 EVALUATION OF THE RESULTS - SAFETY

Additional displacements are generated during a Safety calculation. The totaldisplacements do not have a physical meaning, but the incremental displacements in thefinal step (at failure) give an indication of the likely failure mechanism.


TUTORIAL MANUAL

In order to view the mechanisms in the three different stages of the embankmentconstruction:

Select the last Safety phase and click the View calculation results button.

• From the Deformations menu select Incremental displacements→ |∆u|.Change the presentation from Arrows to Shadings. The resulting plots give a goodimpression of the failure mechanisms (Figure 4.16). The magnitude of thedisplacement increments is not relevant.

Figure 4.16 Shadings of the total displacement increments indicating the most applicable failuremechanism of the embankment in the final stage

The safety factor can be obtained from the Calculation info option of the Project menu.The value of ΣMsf represents the safety factor, provided that this value is indeed more orless constant during the previous few steps.

The best way to evaluate the safety factor, however, is to plot a curve in which theparameter ΣMsf is plotted against the displacements of a certain node. Although thedisplacements are not relevant, they indicate whether or not a failure mechanism hasdeveloped.

In order to evaluate the safety factors for the three situations in this way, follow thesesteps:

• Click the Curves manager button in the toolbar.

• Click New in the Charts tabsheet.

• In the Curve generation window, select the embankment toe (Point A) for the x-axis.Select Deformations→ Total displacements→ |u|.

• For the y -axis, select Project and then select Multipliers→ ΣMsf . The Safetyphases are considered in the chart. As a result, the curve of Figure 4.17 appears.

The maximum displacements plotted are not relevant. It can be seen that for all curves amore or less constant value of ΣMsf is obtained. Hovering the mouse cursor over a pointon the curves, a box showing the exact value of ΣMsf can be obtained.



Figure 4.17 Evaluation of safety factor

4.6 USING DRAINS

In this section the effect of the drains in the project will be investigated. The embankmentconstructions will be redefined by introducing four new phases having the sameproperties as the first four consolidation phases. The differences in the new phases are:

• The drains should be active in all the new phases.

• The Time interval in the first three of the consolidation phases (1 to 3) is 1 day. Thelast phase is set to Minimum pore pressure and a value of 1.0 kN/m2 is assigned tothe minimum pressure (|P-stop|).

After the calculation is finished, select the last phase and click the View calculationresults button. The Output window now shows the deformed mesh after the drained

construction of the final part of the embankment. In order to compare the effect of thedrains, the excess pore pressure dissipation in node B can be used.

Open the Curves manager.

• In the Chart tabsheet double click Chart 1 (pexcess of node B versus time). The chartis displayed. Close the Curves manager.

Click the Settings button in the toolbar. The Settings window pops up.

• Click the Add curve button and select the Add from current project option in theappearing menu. The Curve generation window pops up.

Hint: Instead of adding a new curve, the existing curve can be regenerated usingthe corresponding button in the Curves settings window.

• Select the Invert sign option for y-axis.

• Click OK to accept the selected options and close the Curve generation window.

• In the chart a new curve is added and a new tabsheet corresponding to it is openedin the Settings window.

• Click the Phases button. From the displayed window select the Initial phase and thelast four phases (drains) and click OK.


TUTORIAL MANUAL

• In the Settings click Apply to preview the generated curve.

• Click OK to close the Settings window. The chart (Figure 4.18) gives a clear view ofthe effect of drains in the time required for the excess pore pressures to dissipate.

Figure 4.18 Effect of drains


PHASED EXCAVATION OF A SHIELD TUNNEL

5 PHASED EXCAVATION OF A SHIELD TUNNEL

The lining of a shield tunnel is often constructed using prefabricated concrete ringsegments, which are bolted together within the tunnel boring machine to form the tunnellining. During the erection of the tunnel lining the tunnel boring machine (TBM) remainsstationary. Once a tunnel lining ring has been fully erected, excavation is resumed, untilenough soil has been excavated to erect the next lining ring. As a result, the constructionprocess can be divided in construction stages with a length of a tunnel ring, often about1.5 m long. In each of these stages the same steps are repeated over and over again.

In order to model this, a geometry consisting of slices each 1.5 m long can be used. Thecalculation consists of a number of Plastic phases, each of which models the same partsof the excavation process: the support pressure at the tunnel face needed to preventactive failure at the face, the conical shape of the TBM shield, the excavation of the soiland pore water within the TBM, the installation of the tunnel lining and the grouting of thegap between the soil and the newly installed lining. In each phase the input for thecalculation phase is identical, except for its location, which will be shifted by 1.5 m eachphase.

final lining groutpressure

TBM

contraction of shield

C = 0.5% Cref = 0.5%

Cinc,axial = −0.0667%

Figure 5.1 Construction stages of a shield tunnel model

5.1 GEOMETRY

In the model, only one symmetric half is included. The model is 20 m wide, it extends 80m in the y direction and it is 20 m deep. These dimensions are sufficient to allow for anypossible collapse mechanism to develop and to avoid any influence from the modelboundaries.

When starting PLAXIS 3D set the proper model dimensions in the Project propertieswindow, that is xmin = -20, xmax = 0, ymin = 0 and ymax = 80.


The subsoil consists of three layers. The soft upper sand layer is 2 m deep and extendsfrom the ground surface to Mean Sea Level (MSL). Below the upper sand layer there is aclay layer of 12 m thickness and this layer is underlain by a stiff sand layer that extends toa large depth. Only 6 m of the stiff sand layer is included in the model. Hence, the bottomof the model is 18 m below MSL. Soil layer is assumed to be horizontal throughout the


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model and so just one borehole is sufficient to describe the soil layers. The presentgroundwater head corresponds to the MSL.

Press the Create borehole button and click at the origin of the system of axis tocreate a borehole at (0 0 0). The Modify soil layers window will open.

• Define 3 layers: Upper sand with the top at 2 m and the bottom at 0 m, Clay with thebottom at -12 m and Stiff sand with the bottom at -18 m.

Open the materials database by clicking the Materials button and create the datasets for the soil layers and the final concrete lining in the tunnel as specified in Table5.1.


Parameter Name Upper sand Clay Stiff sand Concrete Unit

General

Material model Model Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Linear elastic −Drainage type Type Drained Drained Drained Non porous −Unit weight abovephreatic level

γunsat 17.0 16.0 17.0 27.0 kN/m3

Unit weight belowphreatic level

γsat 20.0 18.0 20.0 − kN/m3

Parameters

Young'modulus E ' 1.3 · 104 1.0 · 104 7.5 · 104 3.1 · 107 kN/m2

Poisson's ratio ν ' 0.3 0.35 0.3 0.1 −Cohesion c'ref 1.0 5.0 1.0 − kN/m2

Friction angle ϕ' 31 25 31 − ◦

Dilatancy angle ψ 0 0 0 − ◦

Interfaces

Interface strength − Rigid Rigid Rigid Rigid −Initial

K0 determination − Automatic Automatic Automatic Automatic −

• Assign the material data sets to the corresponding soil layers (Figure 5.2) and closethe Modify soil layers window. The concrete data set will be assigned later.

Figure 5.2 Soil layer distribution




The tunnel excavation is carried out by a tunnel boring machine (TBM) which is 9.0 mlong and 8.5 m in diameter.

Create tunnel surfaces

In Structures mode both the geometry of the tunnel and the TBM will be defined. This isdone by creating a polycurve contouring the outside of the tunnel at the inlet of the tunnel:

Click the Create polycurve button in the side toolbar.

• Click anywhere on the draw area to define the insertion point. The Shape designerwindow pops up.

• In the General tabsheet the default option for shape, (Free) is valid for thispolycurve.

• The polycurve is drawn in the xz-plane. Select the Z-axis option in the drop-downmenu for the Orientation axis 2 (Section 5.2.3 of Reference Manual). A screenshotof the General tabsheet after the proper assignment is given in Figure 5.3.

Figure 5.3 General tabsheet of the Shape designer

• Proceed to the Segments tabsheet.

• Click Add to introduce a new segment.

• Change the segment type by selecting the Arc option in the Segment typedrop-down menu.

• Assign a value of 180◦ to the Relative start angle.

• Assign a value of 4.25 m to the Radius.

• Define a Segment angle of 180◦.

• The Discretisation angle is by default set to 5◦. This value will be used in thistutorial. A screenshot of the Sections tabsheet after the proper assignment is givenin Figure 5.4.

• Click OK to complete the definition of the polycurve and close the Shape designer


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Figure 5.4 Sections tabsheet of the Shape designer

Hint: An arc is discretized into line segments (cords). The angle subtended byeach cord along the discretized arc is called the Discretization angle.

window.

• In the Selection explorer set the coordinates of the insertion point to (0 0 -4.75)(Figure 5.5).

Figure 5.5 Polycurve in the Selection explorer

The next step is to create the contour representing the inner diameter of the final lining.Taking into account the thickness of the final lining of 0.25 m, the insertion point will be atz = -5 and the radius of the arc will be 4 m. To create the corresponding polycurve:


• In the General tabsheet the default option for shape is valid for this polycurve.

• The polycurve is drawn in the xz-plane. Select the Z-axis option for the Orientationaxis 2.



• Proceed to the Segments tabsheet and add a new Arc section.

• Assign a value of 180◦ to the Relative start angle.

• Assign a value of 4 m to the Radius.

• Define a Segment angle of 180◦.

• The Discretisation angle is by default set to 5◦. This value will be used in this tutorial.

• Click OK to complete the definition of the polycurve and close the Shape designerwindow. Figure 5.6 displays the defined polycurves in the model.

• Select the created polycurve and set the coordinates of its insertion point to (0 0 -5)in the Selection explorer.

Figure 5.6 Polycurves in the model (front view)

To create the left half of the tunnel:

Multi-select the polycurves and click the Extrude object button in the side toolbar.Assign a value of 41.5 to the y-direction. To have a preview of the extrusion click onone of the input cells in the Extrude window (Figure 5.7). Click Apply to finish theextrusion.

To create the tunnel volume the final intersection plane needs to be defined.

• Right-click the inner polycurve and select the Create surface option from theappearing menu.

• In the same way create a surface for the outer polycurve.

Reorientate the model by clicking the Front view button.

Click the Select multiple objects button in the side toolbar.


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Figure 5.7 Preview of the extrusion

Select the Select surfaces option in the appearing menu. Select the surfacescreated from the polycurves (Figure 5.8).

Figure 5.8 Selection of the surfaces in the model

• Right-click and select the Intersect and recluster option from the appearing menu.The created surfaces will be referred to as A (inner surface) and B (outer surface),as shown in Figure 5.9. Note that the outer surface B corresponds to the lining andthe inner surface A to the interior of the tunnel.

• Multi-select the surfaces created after the intersection.

Click the Create array button. In the Array window set Shape to 1D, y-direction.Keep the default number of columns (2) and set the Distance between the columnsoption to y = 41.5.



B A

Figure 5.9 Inner and outer surfaces

• Delete the initial surfaces at y = 0.

Creating excavation levels for the TBM advancement

Different levels of excavation are considered in order to model the advancement of theTBM. In the calculation 5 phases will be simulated, these being the initial position of theTBM and a forward movement of 4 x 1.5 meters. Therefore vertical planes representingthe initial position of the TBM and final tunnel lining as well as the front and back of theTBM and final tunnel lining in the 4 phases where the TBM moves forward should bedefined. This gives a total of 12 planes varying from y = 25 to y = 41.5 with anintermediate distance of 1.5 m.

• Multi-select the surfaces (A and B) at y = 41.5.

Click the Create array button. In the Array window set the Shape to 1D, y-direction.Set the number of columns to 12 and the distance between the columns to y = -1.5.

Creating tunnel face pressures

The tunnel face pressure is a bentonite pressure that increases linearly with depth. Forthe initial position of the TBM and the successive 4 positions when simulating theadvancement of the TBM a tunnel face pressure (bore front pressure) has to be defined.

• From the 12 surfaces inside the tunnel that were created before, select both theparts A and B of the surfaces located at y = 35.5 to y = 41.5 (a total of 10) (Figure5.10).

• Right-click on one of the selected surfaces and select the Create surface loadoption from the appearing menu.

In the Selection explorer, click the plus sign (+) in front of SurfaceLoad to extend thetree.

• The tunnel face pressure is a bentonite pressure that increases linearly with depth.Set the Distribution of the load to Perpendicular, vertical increment. Assign a valueof 90 kN/m2 to σn,ref and 14 kN/m2/m to σn,inc .

• Assign (0 0 -4.75) to the coordinates of the reference point of the load. Note thatonly the z-coordinate of the reference point is of importance.


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Figure 5.10 Tunnel face pressures in the model

Creating jack forces

In order to move forward during the boring process, the TBM has to push himself againstthe existing tunnel lining. This is done by hydraulic jacks. The force applied by the jackson the final tunnel lining has to be taken into account.

• Select all B parts (Figure 5.9) of the 5 rear most tunnel planes, located at y = 25 to y= 31 as shown in Figure 5.11.

• Right-click on one of the selected surfaces and select the Create surface loadoption in the appearing menu.


• Jack forces are uniform, therefore set the Distribution to Perpendicular and assign ina load of σn = −635.4 kN/m2. Note that this load is negative as it is directedbackwards, in the opposite direction of the face pressure.

Figure 5.11 Selected surfaces for jack forces in the model



Defining the TBM, contraction and grout pressure

After defining the geometry of the tunnel and the TBM, the plate element for the TBMneeds to be defined. To define the TBM:

• Right-click on the outer circular surface and select the Create plate option from theappearing menu to assign a plate element to the surface representing the TBM.

Create a plate material dataset for the TBM according to the Table 5.2 and assign itto the created plate. Note that only a total length of 9.0 m of plates will be active ineach phase to represent the TBM.

Table 5.2 Material properties of the plate representing the TBM

Parameter Name TBM Unit

Thickness d 0.35 m

Material weight γ 120 kN/m3

Material behaviour - Linear; Isotropic -

Young’s modulus E1 23.0·106 kN/m2

Poisson’s ratio ν12 0 -

Shear modulus G12 11.5·106 kN/m2

To define the contraction:

• Right-click the same surface and select the Create surface contraction option fromthe appearing menu. The distribution type and value of the contraction will bespecified when the phases are defined.

The surface load representing the grout pressure will be constant during the buildingprocess and therefore it is possible to define it in the Structures mode so that it is notneeded to change it when the construction phases are defined. In the specifications ofthe tunnel boring process it is given that the grout pressure should be 100 kN/m2 at thetop of the tunnel (z = -4.75) and should increase with 20 kN/m2/m depth. To define thegrout pressure:

• Similarly, right-click the same surface again and select the Create surface load toadd the surface load that will be used as grout pressure.


• Select the Perpendicular, vertical increment option in the Distribution drop-downmenu.

• Set the σn,ref to 100 and σn,inc to 20.

Hint: When a perpendicular load is applied, the sign of the load depends on thelocal perpendicular axis of the surface. A negative sign of the load indicatesa load applied in the direction opposite to the local perpendicular axis.

• Define (0 0 -4.75) as reference point for the load by assigning the values to xref , yrefand zref in the Selection explorer.

Finally, a soil-structure interaction has to be added on the outside of the tunnel.

• Right-click the outer circular surface once more and select the Create positive


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interface option from the appearing menu to add the interface.

Figure 5.12 TBM, contraction and grout pressure in the model

Hint: For drawing purposes it may be practical to hide the interface and the volumerepresenting the lining, so that it will not block the view on the tunnel. Thiscan be done in the Model explorer by clicking on the small "eye" in front ofthe selection (interface of volume) to toggle between showing and hiding it.

This concludes the model creation in Structures mode.

5.2 MESH GENERATION

In the Mesh mode it is possible to specify global and local refinements and generate themesh. In order to generate more accurate results a refinement of the mesh around thewalls and floor should be applied. When entering the mesh mode the total geometry isshown as dark grey.

Click the Generate mesh button in order to generate the mesh. The Mesh optionswindow appears.

• The default option (Medium) will be used to generate the mesh.

Click the View mesh button to inspect the generated mesh (Figure 5.13).

After inspecting the mesh the output window can be closed. Mesh generation has nowbeen finished and so creating all necessary input for defining the calculation phases hasbeen finished.



Figure 5.13 The generated mesh


The excavation of the soil and the construction of the tunnel lining will be modelled in theStaged construction mode. Since water levels will remain constant the Water levels modecan be skipped. It should be noted that due to the mesh generation the tunnel effectivelyhas been split in an upper part, located in the clay, and a lower part located in the stiffsand. As a result, both the lower and the upper part of the tunnel should be considered.

The soil in front of the TBM will be excavated, a support pressure will be applied at thetunnel face, the TBM shield will be activated and the conicity of the shield will bemodelled, at the back of the TBM the pressure due to the back fill grouting will bemodelled as well as the force the hydraulic jacks driving the TBM exert on the alreadyinstalled lining, and a new lining ring will be installed. The first phase differs from thefollowing phases, as in this phase the tunnel is activated for the first time. This phase willmodel a tunnel that has already advanced 25 m into the soil. Subsequent phases willmodel an advancement by 1.5 m each.

5.3.1 INITIAL PHASE

The initial phase consists of the generation of the initial stresses using the K0 procedure.The default settings for the initial phase are valid.

5.3.2 FIRST PHASE - INITIAL POSITION OF THE TBM

In the first phase it is assumed that the TBM has already advanced 25 m. In order toconsider the conicity of the TBM in the first 25 m, the plates representing TBM areactivated and 0.5% contraction is applied. The final lining will be activated in the followingphase.

• Add the first calculation phase.

Select the right view to reorientate the model in order to obtain a clearer view of theinside of the tunnel.

• In the draw area select the soil volumes corresponding to the inside of the tunneland the lining in the first 25 m (Figure 5.14). Note that in the figures representing themodel only the part of the model surrounding the tunnel is displayed.

• In the Selection explorer deactivate the soil. The soil is switched off, but thewireframe representing the deactivated soil is still coloured red as the deactivated


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Figure 5.14 Selection of soil volumes (0 m - 25 m)

soil is still selected.

In the Selection explorer extend the Soil subtree and set WaterConditions to Dry.

Hint: An object that is deactivated will automatically be hidden as a volume orsurface, but a wireframe representing the hidden object will remain. Thevisibility of the object not active in a calculation phase can be defined in thecorresponding tabsheet of the Visualization settings window (Section 3.5.3 ofthe Reference Manual).

To activate the interface, the plate and the contraction in the first 25 m of the tunnel:

Select the Select plates option in the appearing menu. Select the surfaces between0 m and 25 m in the model to which plates are assigned (Figure 5.15).

Figure 5.15 Selection of plate (0 m - 25 m)

• In the Selection explorer activate plate, positive interfaces and contraction bychecking the corresponding boxes.

In the Selection explorer extend the Contraction subtree and specify a uniformcontraction of 0.5%.

The section next to the first 25 m (section 25 m - 26.5 m), will represent the area directlybehind the TBM were grout is injected in the tail void. The soil inside the tunnel and thelining will be deactivated whereas the surface load representing the grout pressure will be



activated.

• Select the volumes corresponding to the lining and the inside of the tunnel between25 m and 26.5 m (Figure 5.16).

• In the Selection explorer deactivate the selected soil volumes and setWaterConditions to Dry.

Figure 5.16 Selection of soil volumes (25 m - 26.5 m)

In this section, the plate, the positive interface and the contraction will not be activated. Inorder to differentiate among the surface loads defined in the model, the Select plateoption will be used to select only the surfaces where plate, interface, contraction andgrouting pressure is assigned.

Select the surfaces between 25 m and 26.5 m in the model by defining a rectangleas shown in Figure 5.17.

• In the Selection explorer activate the load corresponding to the grouting. Note thatthe proper settings were already defined in the Structures mode.

Figure 5.17 Selection of plates (25 m - 26.5 m)

In the next 6 sections (26.5 m - 35.5 m) the TBM will be modelled.

Select the soil volumes corresponding to the lining and the soil inside the tunnel forthe next 6 sections lying between y = 26.5 m and y = 35.5 m (Figure 5.18).

• In Selection explorer deactivate the soil and set WaterConditions to Dry.

Select the surfaces between 26.5 m and 35.5 m in the model to which plates areassigned.


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Figure 5.18 Selection of soil volumes (26.5 m - 35.5 m)

• In the Selection explorer activate the positive interface, the plate and the contraction.

The TBM has a slight cone shape. Typically, the cross sectional area at the tail of theTBM is about 0.5% smaller than the front of the TBM. The reduction of the diameter isrealized over the first 7.5 m length of the TBM (35.5 m to 28 m) while the last 1.5 m to thetail (28 m to 26.5 m) has a constant diameter. This means that the section (28 m to 26.5m) has a uniform contraction of 0.5% and the remaining 5 sections have a linearcontraction with a reference value cref = 0.5%, and increment cinc,axial = -0.0667% and areference point with y -coordinate equal to 28.

Select the surfaces between 26.5 m and 28 m. Assign a Uniform contraction of0.5%.

• Select the surfaces between 28 m and 35.5 m.

• In the Selection explorer select the Axial increment option for the contractiondistribution and define Cref = 0.5% and Cinc,axial = -0.0667%/m. The increment mustbe a negative number, because the contraction decreases in the direction of thepositive local 1-axis. The reference location is (0 28 0).

The last part of this first calculation phase that has to be defined is the tunnel phasepressure to keep the tunnel phase stable:

Select the surface load corresponding to the phase pressure at y = 35.5. An overallview of the model and a local detail is shown in Figure 5.19.

• In the Selection explorer activate the surface load. The distribution of the load isalready set to Perpendicular, vertical increment and the value is specified as σn,ref =90 and σn,inc = 14 when the geometry was defined in the Structures mode. Thereference location is (0 0 -4.75).

Click the Preview button to get a preview of everything that has been defined(Figure 5.20). Make sure that both grout pressure and tunnel face pressure areapplied and that both increase from top to bottom.



Figure 5.19 Tunnel phase pressure selection at y = 35.5

Figure 5.20 Preview of the Phase 1

5.3.3 SECOND PHASE - TBM ADVANCEMENT 1

In this phase the advancement of the TBM by 1.5 m will be modelled.

• Add a new phase.

• Hide the soil outside the tunnel, so that the TBM, lining, surface loads andcontraction can be accessed from both the outside and the inside of the tunnel.

Select the plates between 0 m and 25 m and deactivate the assigned plate andcontraction.

Select volumes corresponding to the tunnel lining between 0 m and 25 m.

In the Selection explorer extend the Soil subtree.

• Activate the soil.

• Click the material and select the Concrete option from the drop-down menu.

• Select the load assigned between 25 m and 26.5 m by directly clicking the modeland deactivate it.

• Activate the positive interface between 25 m and 26.5 m.

Select volumes between 25 m and 26.5 m and follow the same steps as previous todefine the final lining.

Select the jack force at y = 26.5 m (Figure 5.21) and activate it.

As the TBM has advanced by 1.5 m, only grouting is applied to the section between y =26.5 and y = 28. In this section the plate, the interface and the contraction will bedeactivated.

• Select the surfaces between 26.5 m and 28 m in the model and deactivate the


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Figure 5.21 Jack force at y = 26.5 m

interface, the plate and the contraction.

• Activate the load corresponding to the grouting.

The following 6 sections (28 m to 37 m) correspond to the TBM.

• The section between y = 28 m and y = 29.5 m, is the tail of the TBM. Select the twoparts of the plate element that form the TBM and modify the assigned contraction toUniform and assign a value of Cref = 0.5%.

Deactivate the tunnel pressure (y = 35.5 m) for Phase 1.

• The section between y = 35.5 m and y = 37 m is excavated in this phase. Deactivatethe soil in the volumes inside the tunnel and the ones corresponding to the tunnellining and set the WaterConditions to Dry.

• Activate the interfaces, plate and contraction in the section between y = 35.5 m andy = 37 m.

• Select the surfaces corresponding to the TBM between y = 29.5 m and y = 37 m anddefine the contraction as done in the Phase 1 for the contraction in the sectionsbetween y = 28 m and y = 35.5 m.

• Activate the tunnel phase pressure at y = 37 m. This completes the definition of thefirst step of TBM advance.

5.3.4 THIRD PHASE - TBM ADVANCEMENT 2

The third phase implies another advance of the TBM. Hence in principle the same actionsas done in the previous phase have to be applied, but one section further forward.

• Add a new phase.

• The section between 0 m and 25 m is the intact tunnel. No changes have to bedone. Section between 25 m and 26.5 m is intact tunnel as well, however the jackforces on the side of this section have to be deactivated. Select the side of thesection and in Selection explorer deactivate the surface load representing the jackforces at y = 26.5 m.

• Deactivate the surface load between 26.5 m to 28 m that represents the groutpressure and activate the interface.

• Select the volumes representing the final lining (between 26.5 m to 28 m). Assignthe Concrete material set to the final lining that was just activated.

• Select the surfaces representing the jack forces at y = 28 (Figure 5.22) and activatethem.



Figure 5.22 Jack forces to be activated at y = 28

Section between y = 28 m to y = 29.5 m has to be changed from the tail of the TBM togrout pressure.

• Select the two parts that represent the TBM and deactivate the plate representingthe TBM, the surface contraction and the interface while activating the surface loadrepresenting the grout pressure.

• The section between y = 29.5 m and y = 31 m, is the tail of the TBM. Select the twoparts of the plate element that form the TBM and modify the assigned contraction toUniform and assign a value of Cref = 0.5%.

Deactivate the tunnel phase pressure (y = 37 m) for Phase 2.

• The section between y = 37 m and y = 38.5 m is excavated in this phase. Deactivatethe soil in the volumes inside the tunnel and the ones corresponding to the tunnellining and set the WaterConditions to Dry.

• Activate the interfaces, plate and contraction in the section between y = 37 m and y= 38.5 m.

• Select the contraction between y = 31 m and y = 38.5 m and define the contractionas done in the Phase 1 for the contraction in the section between y = 28 m and y =35.5 m.

• Activate the tunnel phase pressure at y = 38.5 m.

5.3.5 FOURTH PHASE - TBM ADVANCEMENT 3

In this phase the TBM advances from y = 38.5 to y = 40. The same steps as for the thirdphase will be followed, taking into account that sections 1 and 2 (y = 0 to y = 26.5) remainunchanged, the jack forces at y = 28 should be removed, the section 4 (y = 28 to y =29.5) should be changed from grout pressure to final tunnel lining and jack forces mustbe applied, the section 5 (y = 29.5 to y = 31) should be changed from the tail of the TBMto grout pressures etc. until the section between y = 38.5 to y = 40, which is the newlyexcavated tunnel section.

5.3.6 FIFTH PHASE - TBM ADVANCEMENT 4

In this phase the final advancement of the TBM is modelled. The same steps as for thethird phase will be followed, taking into account that sections 1 to 3 (y = 0 to y = 28)remain unchanged, the jack forces at y = 29.5 are removed, the section 5 (y = 29.5 to y =31) should be changed from grout pressure to final tunnel lining and jack forces must beapplied, the section 6 should be changed from the tail of the TBM to grout pressures etc.until the final section.

Press the Calculate button to start the calculation. Ignore the message "No nodes or


TUTORIAL MANUAL

stress points selected for curves" as we will not draw any load-displacement curves inthis example, and continue the calculation.


Once the calculation has been completed, the results can be evaluated in the Outputprogram. In the Output program the displacement and stresses are shown in the full 3Dmodel, but the computational results are also available in tabular form. To view theresults for the current analysis, follow these steps:

• Select the last calculation phase (Phase 5) in the Phases explorer.

• Click on the Output button to open the Output program. The Output program will bydefault show the 3D deformed mesh at the end of the selected calculation phase.

• From the Deformations menu, select Total displacements and then uz in order tosee the total vertical displacements in the model as a shaded plot (Figure 5.23).

Figure 5.23 Total vertical displacements after the final phase uz ≈ 3cm

In order to see the settlements at ground level make a horizontal cross section bychoosing the Horizontal cross section button. In the window that appears fill in a crosssection height of 1.95 m. The window with the cross section opens (Figure 5.24). Themaximum settlement at ground level is about 2 cm.

Figure 5.24 Settlement trough at ground level |u| ≈ 2cm


RAPID DRAWDOWN ANALYSIS

6 RAPID DRAWDOWN ANALYSIS

This example concerns the stability of a reservoir dam under conditions of drawdown.Fast reduction of the reservoir level may lead to instability of the dam due to high porewater pressures that remain inside the dam. The dam to be considered is 30 m high. Thetop width and the base width of the dam are 5 m and 172.5 m respectively. The damconsists of a clay core with a well graded fill at both sides. The geometry of the dam isdepicted in Figure 6.1. The normal water level behind the dam is 25 m high. A situation isconsidered where the water level drops 20 m. The normal phreatic level at the right handside of the dam is 10 m below ground surface. The sub-soil consists of overconsolidatedsilty sand.

x

y

50 m 77.5 m

5 m

5 m

25 m

20 m 120 m120 m

37.5 m

30 m

30 m

90 m

Core

FillFill

Subsoil

Figure 6.1 Geometry of the dam

Objectives:

• Performing fully coupled flow deformation analysis

• Defining time-dependent hydraulic conditions

• Using unsaturated flow parameters

6.1 GEOMETRY

• Start the Input program and select the Start a new project from the Quick selectdialog box.

• In the Project properties window enter a proper title.

• Keep the default units and set the model dimensions to xmin = −130, xmax = 130,ymin = 0 and ymax = 50.

Assuming the dam is located in a wide valley, a representative length of 50 m isconsidered in the model in order to decrease the model size. The geometry of the modelis shown in Figure 6.2.


In order to define the underlying foundation soil, a borehole needs to be added andmaterial properties must be assigned. A layer of 30 m overconsolidated silty sand isconsidered as sub-soil in the model.

Create a borehole at (0.0 0.0). The Modify soil layers window pops up.


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Figure 6.2 The geometry of the model

• Add a soil layer extending from ground surface (z = 0) to a depth of 30 m (z= -30).

• Set the Head in the borehole to -10 m. A horizontal water level will be automaticallygenerated. This water level in combination with surface groundwater flow boundaryconditions will be used in the Fully coupled flow deformation analyses.


• Create data sets under Soil and interfaces set type according to the informationgiven in Table 6.1. Note that the Interfaces and Initial tabsheets are not relevant (nointerfaces or K0 procedure used).

• Assign the Subsoil material dataset to the soil layer in the borehole.

Table 6.1 Material properties of the dam and sub-soil

Parameter Name Core Fill Subsoil Unit

General

Material model Model MohrCoulomb

MohrCoulomb

MohrCoulomb

-

Drainage type Type Undrained B Drained Drained -

Soil unit weight above p.l. γunsat 16.0 16.0 17.0 kN/m3

Soil unit weight below p.l. γsat 18.0 20.0 21.0 kN/m3

Parameters

Young's modulus E ' 1.5·103 2.0·104 5.0·104 kN/m2

Poisson's ratio ν ' 0.35 0.33 0.3 -

Cohesion c'ref - 5.0 1.0 kN/m2

Undrained shear strength su,ref 5.0 - - kN/m2

Friction angle ϕ' - 31 35.0 ◦

Dilatancy angle ψ - 1.0 5.0 ◦

Young's modulus inc. E 'inc 300 - - kN/m2

Reference level zref 30 - - m

Undrained shear strength inc. su,inc 3.0 - - kN/m2

Reference level zref 30 - - m

Flow

Flow data set Model Hypres Hypres Hypres -

Model - VanGenuchten

VanGenuchten

VanGenuchten

-

Soil - Subsoil Subsoil Subsoil -

Soil coarseness - Very fine Coarse Coarse -

Horizontal permeabilitykx 1.0·10-4 0.25 0.01 m/day

ky 1.0·10-4 0.25 0.01 m/day

Vertical permeability kz 1.0·10-4 0.25 0.01 m/day

6.1.2 DEFINITION OF THE EMBANKMENT

The embankment will be defined in the Structures mode.



Define a surface by specifying points located at (-80 0 0), (92.5 0 0), (2.5 0 30) and(-2.5 0 30).

Define a surface by specifying points located at (-10 0 0), (10 0 0), (2.5 0 30) and(-2.5 0 30).

• Multi-select the created surfaces and right-click on the draw area. Select theIntersect and recluster option from the appearing menu.

• Multi-select the surfaces and extrude along (0 50.0 0) The volumes representing thedam are generated.

• Delete the surfaces used to create the soil volumes.

• Assign the corresponding material datasets to the soil volumes.

Time dependent conditions can be assigned to surface groundwater flow boundaryconditions. Define surface groundwater flow boundary conditions (under the Createhydraulic conditions tool) according to the information in Table 6.2.

Table 6.2 Surface groundwater flow boundary conditions

Surface Points

1 (-130 0 0), (-80 0 0), (-80 50 0), (-130 50 0)

2 (-80 0 0), (-2.5 0 30), (-2.5 50 30), (-80 50 0)

3 (-130 0 0), (-130 0 -30), (-130 50 -30), (-130 50 0)

6.2 MESH GENERATION

For the generation of the mesh it is advisable to set the Element distribution parameter toFine. To modify the global coarseness:

Click the Generate mesh button in the side toolbar. The Mesh options window isdisplayed.

• Select the Fine option form the Element distribution drop-down (Figure 6.3).

Figure 6.3 Modification of the Global coarseness

• Click OK to close the Mesh options window and to generate the mesh.

Click the View mesh button in the side toolbar to preview the mesh. The resultingmesh is displayed in Figure 6.4.


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Figure 6.4 The resulting mesh


In the calculation process the initial state (high reservoir), the rapid drawdown case, theslow drawdown case and finally the low water level case will be considered. A safetyanalysis will be performed for each of the cases.

• Proceed to the Water levels mode.

Create water levels corresponding to the full reservoir and the low water level casesaccording to the information given in Table 6.3.

• In the Attributes library of the Model explorer rename the created user water levelsas 'High_Reservoir' and 'Low_Reservoir'.

Table 6.3 Water levelsLevel Points

High reservoir (-130 0 25), (-10 0 25), (93 0 -10), (130 0 -10), (130 50 -10), (93 50 -10), (-10 50 25), (-130 50 25)

Low reservoir (-130 0 5), (-10 0 5), (93 0 -10), (130 0 -10), (130 50 -10), (93 50 -10), (-10 50 5), (-130 50 5)

Hint: No modifications, such as Time dependency is possible for Borehole waterlevels and non-horizontal User water levels.

6.3.1 INITIAL PHASE: HIGH RESERVOIR

• Proceed to the Staged construction mode.

• Double-click the initial phase in the Phases explorer.

• In the General subtree of the Phases window rename the phase as 'High reservoir'.

Select the Gravity loading option as Calculation type. Note that Staged constructionis the only option available for Loading type.

Select the Steady state groundwater flow option as pore pressure calculation type.

• Note that the options Ignore undr. behaviour (A,B) and Ignore suction are by defaultselected in the Deformation control parameters subtree. The default values will beused for the parameters in the Numerical control parameters and Water controlparameters subtrees.


• In the Staged construction mode activate the soil clusters representing theembankment.




• In the GroundwaterFlow subtree set BoundaryYMin, BoundaryYMax andBoundaryZMin to Closed. The remaining boundaries should be Open (Figure 6.5).

• In the Water subtree select the high reservoir water level (High_Reservoir) asGlobalWaterLevel.

Figure 6.5 Boundary conditions for groundwater flow

6.3.2 PHASE 1: RAPID DRAWDOWN

In the rapid drawdown phase the water level in the reservoir will be lowered from z = 25 mto z = 5 m in a period of 5 days. To define the function describing the fluctuation of thewater level:

• Extend the Attributes library in the Model explorer.

• Right click on Flow functions and select the Edit option in the appearing menu. TheFlow functions window is displayed.

In the Head functions tabsheet add a new function by clicking the correspondingbutton. The new function is highlighted in the list and options to define the functionare displayed.

• Specify a proper name to the function for the rapid drawdown (e.g. Rapid).

• Select the Linear option from the Signal drop-down menu.

• Assign a value of -20 m to ∆ Head, representing the amount of the head decrease.

• Specify a time interval of 5 days. A graph is displayed showing the defined function(Figure 6.6).

• Click OK to close the Flow functions window.

Add a new calculation phase and rename it (e.g. Rapid drawdown).

Set the Calculation type to Fully coupled flow-deformation.

• Set the Time interval to 5 days.


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Figure 6.6 The flow function for the rapid drawdown case

• In the Deformation control parameters subtree, select the Reset displacements tozero option.


• Activate all the surface groundwater flow boundary conditions.

• Multi-select the surface groundwater flow BCs in the draw area.

• In the Selection explorer select the Head option as behaviour. The distribution ofthe head is Constant. Assign a value of 25 m to href .

• Set the time dependency to Time dependent and select the Rapid option as Headfunction. Information related to the head function is displayed in the Object explorersas well (Figure 6.7).

Figure 6.7 Definition of SurfaceGWFlowBC for the rapid drawdown case

• In the Water subtree in the Model explorer select the BoreholeWaterLevel_1 optionas GlobalWaterLevel.



6.3.3 PHASE 2: SLOW DRAWDOWN

In the slow drawdown phase the water level in the reservoir will be lowered from z = 25 mto z = 5 m in a period of 50 days. To define the function describing the fluctuation of thewater level:

• Create a new flow function following the steps previously described.

• Specify a proper name to the function for the slow drawdown (e.g. Slow).

• Select the Linear option from the Signal drop-down menu.

• Assign a value of -20 m to ∆ Head, representing the amount of the head decrease.

• Specify a time interval of 50 days. The window displaying the defined function isshown in Figure 6.8.

Figure 6.8 The flow function for the slow drawdown case

• Click OK to close the Flow functions window.

Add a new calculation phase and rename it (e.g. Slow drawdown).

• Set the Start from phase parameter to High reservoir.

Set the Calculation type to Fully coupled flow-deformation.

• Set the Time interval option to 50 days.

• In the Deformation control parameters subtree, select the Reset displacements tozero option.


• In the model multi-select all the surface groundwater flow BCs.

• In the Selection explorer select the Slow option as Head function.


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• The BoreholeWaterLevel_1 option is still valid as GlobalWaterLevel.

Phase 3: Low level

This phase considers the steady-state situation of a low reservoir level.

Add a new calculation phase.

• In the Phases explorer double-click the newly added phase. The Phases window isdisplayed.

• In the General subtree specify the name of the phase (ex: Low level).

• Set the Start from phase parameter to High reservoir.

Select the Plastic option as calculation type.

Select the Steady state groundwater flow option as Pore pressure calculation type

• In the Deformation control subtree, select Ignore und. behaviour (A,B) and Resetdisplacements to zero.


• In the Model explorer Deactivate the surface groundwater flow BSs.

• In the Water subtree select the low reservoir water level (Low_Reservoir) asGlobalWaterLevel.

Phase 4 to 7:

In Phases 4 to 7 stability calculations are defined for the previous phases respectively.

Select the phase in the Phases explorer. Add a new calculation phase and proceedto the Phases window.

Set Calculation type to Safety. The Incremental multipliers option is valid as Loadingtype.

• In the Deformation control subtree, select Reset displacements to zero.

• In the Numerical control parameters subtree set the Max steps parameter to 30 forPhase 4 and to 50 for phases 5 to 7. The final view of the Phases explorer is givenin Figure 6.9.

Figure 6.9 The final view of the Phases explorer

In the Staged construction mode select a nodes located at the crest (-2.5 25.0 30.0 ).



Start the calculation process by clicking the Calculate button in the Stagedconstruction mode.


6.4.1 RESULTS

After the calculation is finished click the View the calculation resultsbutton. The Output window now shows the deformed mesh for the selected phase.

• In the Stresses menu point the Pore pressures option and select the pwater optionfrom the appearing menu.

Define a vertical cross section passing through (-130 15) and (130 15)

The results of the four groundwater flow calculations in terms of pore pressure distributionare shown in Figures 6.10 to 6.13. Four different situations were considered:

• The situation with a high (standard) reservoir level (Figure 6.10).

Figure 6.10 Pore water pressure distribution for high reservoir level

• The situation after rapid drawdown of the reservoir level (Figure 6.11).

Figure 6.11 Pore water pressure distribution after rapid drawdown

• The situation after slow drawdown of the reservoir level (Figure 6.12).

Figure 6.12 Pore water pressure distribution after slower drawdown (phase 3)

• The situation with a low reservoir level (Figure 6.13).


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Figure 6.13 Pore water pressure distribution for low reservoir level (phase 4)

When the change of pore pressure is taken into account in a deformation analysis, someadditional deformation of the dam will occur. These deformations and the effective stressdistribution can be viewed on the basis of the results of phases 1 to 4.

In this tutorial attention is focused on the variation of the safety factor of the dam for thedifferent situations. Therefore, the development of ΣMsf is plotted for the phases 4 to 7as a function of the displacement of the dam crest point (see Figure 6.14).

Figure 6.14 Safety factors for different situations

Rapid drawdown of a reservoir level can reduce the stability of a dam significantly. Fullycoupled flow-deformation and stability analysis can be performed with PLAXIS 3D toeffectively analyze such situations.


DYNAMIC ANALYSIS OF A GENERATOR ON AN ELASTIC FOUNDATION

7 DYNAMIC ANALYSIS OF A GENERATOR ON AN ELASTIC FOUNDATION

In this tutorial the influence of a vibrating source on its surrounding soil is studied. Toreduce the calculation time, only one-quarter of the overall geometry is modelled, usingsymmetry boundary conditions along the lines of symmetry. The physical damping due tothe viscous effects is taken into consideration via Rayleigh damping. Also, due to radialwave propagation, 'geometric damping' can be significant in attenuating the vibration.

The modelling of the boundaries is one of the key points in the dynamic calculation. Inorder to avoid spurious wave reflections at the model boundaries (which do not exist inreality), special conditions have to be applied in order to absorb waves reaching theboundaries.

7.1 GEOMETRY

The vibrating source is a generator founded on a 0.2 m thick concrete footing of 1 m indiameter, see Figure 7.1. Oscillations caused by the generator are transmitted throughthe footing into the subsoil. These oscillations are simulated as a uniform harmonicloading, with a frequency of 10 Hz and amplitude of 10 kN/m2. In addition to the weight ofthe footing, the weight of the generator is modelled as a uniformly distributed load of 8kN/m2.

0.5 m

20 m

20 mGenerator

sandy clay

x

z

z = 0

z = -10

10 m

Figure 7.1 Generator founded on elastic subsoil

The model boundaries should be sufficiently far from the region of interest, to avoiddisturbances due to possible reflections. Although special measures (absorbentboundaries) are adopted in order to avoid spurious reflections, there is always a smallinfluence and it is still a good habit to put boundaries far away. In a dynamic analysis,model boundaries are generally taken further away than in a static analysis.

7.1.1 GEOMETRY MODEL

• Start the Input program and select the Start a new project from the Quick selectdialog box.

• In the Project properties window enter a proper title.


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• Keep the default units and set the model dimensions to xmin = 0, xmax = 20, ymin = 0and ymax = 20. The geometry model is shown in Figure 7.2.

Figure 7.2 Geometry of the model


The subsoil consists of one layer with a depth of 10 m. The ground level is defined at z =0. Create the material dataset according to Table 7.1 and assign it to the soil layer. Notethat water conditions are not considered in this example and the hydraulic head is set at z= -10.


Parameter Name Sandy clay Unit

General

Material model Model Linear elastic −Drainage type Type Drained −Unit weight above phreatic level γunsat 20.0 kN/m3

Unit weight below phreatic level γsat 20.0 kN/m3

Parameters

Young'modulus E ' 5 · 104 kN/m2

Poisson's ratio ν ' 0.3 −Interfaces

Interface strength − Rigid −Initial

K0 determination − Manual −Lateral earth pressure coefficient K0 0.5 −


The generator is defined in the Structures mode. The Polycurve feature is used to definethe geometry.


• In the General tabsheet the default option for shape (Free) and the defaultorientation axes (x-axis, y-axis) are valid for this polycurve.

• In the Segments tabsheet three segments are defined as given in Table 7.2. The



insertion point is located at (0 0 0).

Table 7.2 Segments composing the polycurve

Segment Segment 1 Segment 2 Segment 3

Segment type Line Arc Line

Segment properties

Relative start angle = 90◦

Relative start angle = 0◦ Radius = 0.5 m Relative start angle = 90◦

Length = 0.5 m Segment angle = 90◦ Length = 0.5 m

Discretization angle = 5◦

• Right-click the polycurve and select the Create surface option from the appearingmenu.

• Right-click the created surface and select the Create surface load option in theappearing menu.


• The Uniform distribution is valid. Assign (0 0 -8) to the pressure components.

Definition of dynamic multipliers

Dynamic loads are defined on the basis of input values of loads or prescribeddisplacements and corresponding time-dependent multipliers.

To create the multipliers of the dynamic load:

• In the Model explorer expand the Attributes library subtree.

• Right-click the Dynamic multipliers subtree and select the Edit option from theappearing menu. The Multipliers window pops up.

• Click the Load multipliers tab.

Click Add button to introduce a multiplier for the loads.

• Define a Harmonic signal with an Amplitude of 10, a Frequency of 10 Hz and aPhase of 0◦ as shown in Figure 7.3.

In the Selection explorer, click the plus sign (+) in front of DynSurfaceLoad_1 toextend the dynamic load subtree.

• Specify the components of the load as (0 0 -1). Click Multiplier_z in the dynamicload subtree and select the LoadMultiplier_1 option from the appearing menu.

Hint: The dynamic multipliers can be defined in the Geometry modes as well as inthe Calculation modes.


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Figure 7.3 Definition of a Harmonic multiplier

7.2 MESH GENERATION


• Refine the surface corresponding to the generator by assigning a Fineness factor of0.125.

Click the Generate mesh button. The Medium option will be used for Elementdistribution.

View the generated mesh.

Figure 7.4 Geometry and mesh



Hint: In all dynamic calculations, the user should pay special attention to theelement size to decrease numerical dispersion of waves. It should be notedthat large elements are not able to transmit high frequencies. Thetransmission of waves is governed by both wave speed and wave length. Ifdynamic input contains high frequencies, either high frequencies should befiltered out or a finer mesh should be used.


The calculation consists of 4 phases. The initial phase consists of the generation of theinitial stresses using the K0 procedure. The second phase is a Plastic calculation wherethe static load is activated. The third phase is a Dynamic calculation where the effect ofthe functioning generator is considered. The fourth and final phase is a Dynamiccalculation as well where the generator is turned off and the soil will vibrate freely.

Initial phase


• The initial phase has already been introduced. The default settings of the initialphase will be used in this tutorial.

Phase 1

Add a new phase (Phase_1). The default settings of the added phase will be usedfor this calculation phase.

• In the Staged construction mode activate the static component of the surface load.Do not activate the dynamic load (Figure 7.5).

Figure 7.5 Applied load in the Phase_1


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Phase 2

Add a new phase (Phase_2).

In the General subtree in the Phases window, select the Dynamic option ascalculation type.

• Set the Time interval parameter to 0.5 s.

• In the Deformation control parameters subtree in the Phases window select theReset displacement to zero parameter. The default values of the remainingparameters will be used for this calculation phase.

• In the Staged construction mode activate the dynamic component of the surfaceload. Note that the static component of the load is still active (Figure 7.6).

Figure 7.6 Applied load in the Phase_2

Special boundary conditions have to be defined to account for the fact that in reality thesoil is a semi-infinite medium. Without these special boundary conditions the waveswould be reflected on the model boundaries, causing perturbations. To avoid thesespurious reflections, viscous boundaries are specified at Xmax, Ymax and Zmin. Thedynamic boundaries can be specified in the Dynamics subtree located under the Modelconditions in the Model explorer (Figure 7.7).

Figure 7.7 Boundary conditions for Dynamic calculations



Phase 3


In the General subtree in the Phases window, select the Dynamic option ascalculation type.

• Set the Time interval parameter to 0.5 s.

• In the Staged construction mode deactivate the dynamic component of the surfaceload. Note that the static load is still active. The dynamic boundary conditions of thisphase should be the same as in the previous phase. Figure 7.8 shows the Phasesexplorer of this tutorial.

Select nodes located at the ground surface (ex: (1.4 0 0), (1.9 0 0), (3.6 0 0)) toconsider in curves.

Execute the calculation.

Save the project.


7.3.1 ADDITIONAL CALCULATION WITH DAMPING

In a second calculation, material damping is introduced by means of Rayleigh damping.Rayleigh damping can be entered in the material data set. The following steps arenecessary:

• Save the project under another name.

• Open the material data set of the soil.

• In the General tabsheet click the box next to the Rayleigh α parameter. Note that thedisplay of the General tabsheet has changed displaying the Single DOF equivalencebox.

• Set the value of the ξ parameter to 5% for both targets.

• Set the frequency values to 9 and 11 for the Target 1 and Target 2 respectively.

• Click on one of the definition cells of the Rayleigh parameters. The values of α andβ are automatically calculated by the program.

• Click OK to close the data base.

• Check whether the phases are properly defined (according to the information givenbefore) and start the calculation.


TUTORIAL MANUAL

Figure 7.9 Input of Rayleigh damping


The Curve generator feature is particularly useful for dynamic analysis. You can easilydisplay the actual loading versus time (input) and also displacements, velocities andaccelerations of the pre-selected points versus time. The evolution of the definedmultipliers with time can be plotted by assigning Dynamic time to x-axis and uz to they-axis. Figure 7.10 the response of the pre-selected points at the surface of the structure.It can be seen that even with no damping, the waves are dissipated which can beattributed to the geometric damping.

The presence of damping is clear in Figure 7.11. It can be seen that the vibration istotally seized when some time is elapsed after the removal of the force (at t = 0.5 s).Also, the displacement amplitudes are lower. Compare Figure 7.11 (without damping)with Figure 7.11 (with damping).

It is possible in the Output program to display displacements, velocities and accelerationsat a particular time, by choosing the appropriate option in the Deformations menu. Figure7.12 shows the total accelerations in the soil at the end of phase 2 (t = 0.5 s).



Figure 7.10 Vertical displ.- time on the surface at different distances to the vibrating source (withoutdamping)

Figure 7.11 Vertical displ.- time (with damping)


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Figure 7.12 Total accelerations in the soil at the end of phase 2 (with damping)


FREE VIBRATION AND EARTHQUAKE ANALYSIS OF A BUILDING

8 FREE VIBRATION AND EARTHQUAKE ANALYSIS OF A BUILDING

This example demonstrates the natural frequency of a long five-storey building whensubjected to free vibration and earthquake loading.

The building consists of 5 floors and a basement. It is 10 m wide and 17 m high includingthe basement. The total height from the ground level is 5 x 3 m = 15 m and the basementis 2 m deep. A value of 5 kN/m2 is taken as the weight of the floors and the walls. Thebuilding is constructed on a clay layer of 15 m depth underlayed by a deep sand layer. Inthe model, 25 m of the sand layer will be considered.

8.1 GEOMETRY

The length of the building is much larger than its width and the earthquake is supposed tohave a dominant effect across the width of the building. Taking these facts intoconsideration, a representative section of 3 m will be considered in the model in order todecrease the model size. The geometry of the model is shown in Figure 8.1.

8.1.1 GEOMETRY MODEL

• Start the Input program and select Start a new project from the Quick select dialogbox.

• In the Project tabsheet of the Project properties window, enter an appropriate title.

• Keep the default units and set the model dimensions to Xmin = −80, Xmax = 80, Ymin= 0 and Ymax = 3.

15 m

15 m

25 m

3 m

Figure 8.1 Geometry of the model


The subsoil consists of two layers. The Upper clayey layer lies between the ground level(z = 0) and z = -15. The underlying Lower sandy layer lies to z = -40. Define the phreaticlevel by assigning a value of -15 to the Head in the borehole. Create the material datasetaccording to Table 8.1 and assign it to the corresponding soil layers. The upper layer


TUTORIAL MANUAL

consists of mostly clayey soil and the lower one consists of sandy soil. The presence ofthe groundwater is neglected.

Table 8.1 Material properties of the subsoil layers

Parameter Name Upper clayey layer Lower sandy layer Unit

General

Material model Model HS small HS small -

Drainage type Type Drained Drained -

Soil unit weight above phreatic level γunsat 16 20 kN/m3

Soil unit weight above phreatic level γsat 20 20 kN/m3

Parameters

Secant stiffness in standard drained triaxial test E ref50 2.0·104 3.0·104 kN/m2

Tangent stiffness for primary oedometer loading E refoed 2.561·104 3.601·104 kN/m2

Unloading / reloading stiffness E refur 9.484·104 1.108·105 kN/m2

Power for stress-level dependency of stiffness m 0.5 0.5 -

Cohesion c'ref 10 5 kN/m2

Friction angle ϕ' 18.0 28.0 ◦

Dilatancy angle ψ 0.0 0.0 ◦

Shear strain at which Gs = 0.722G0 γ0.7 1.2·10-4 1.5·10-4 -

Shear modulus at very small strains Gref0 2.7·105 1.0·105 kN/m2

Poisson's ratio ν 'ur 0.2 0.2 -

When subjected to cyclic shear loading, the HS small model will show typical hystereticbehaviour. Starting from the small-strain shear stiffness, Gref

0 , the actual stiffness willdecrease with increasing shear. Figures 8.2 and 8.3 display the Modulus reductioncurves, i.e. the decay of the shear modulus with strain.

0

100000

50000

150000

200000

250000

She

arm

odul

us

Shear strain0.00001 0.0001 0.001 0.01

Gt Gsγ0.7

0.722G0

G used

Figure 8.2 Modulus reduction curves for the upper clayey layer



20000

40000

60000

80000

100000

She

arm

odul

us

Shear strain0.00001 0.0001 0.001 0.01

GtGs

γ0.7

0.722G0

G used

Figure 8.3 Modulus reduction curve for the lower sandy layer

In the HS small model, the tangent shear modulus is bounded by a lower limit, Gur .

Gur =Eur

2(1 + νur )

The values of Grefur for the Upper clayey layer and Lower sandy layer and the ratio to Gref

0are shown in Table 8.2. This ratio determines the maximum damping ratio that can beobtained.

Table 8.2 Gur values and ratio to Gref0

Parameter Unit Upper clayeylayer

Lower sandylayer

Gur kN/m2 39517 41167

Gref0 /Gur - 6.75 2.5

Figures 8.4 and 8.5 show the damping ratio as a function of the shear strain for thematerial used in the model. For a more detailed description and elaboration from themodulus reduction curve to the damping curve can be found in the literature∗.

0

0.2

0.15

0.1

0.05Dam

ping

ratio

Cyclic shear strain0.00001 0.0001 0.001 0.01

Figure 8.4 Damping curve for the upper clayey layer

∗ Brinkgreve, R.B.J., Kappert, M.H., Bonnier, P.G. (2007). Hysteretic damping in small-strain stiffness model. InProc. 10th Int. Conf. on Comp. Methods and Advances in Geomechanics. Rhodes, Greece, 737− 742


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0

0.2

0.15

0.1

0.05D

ampi

ngra

tio

Cyclic shear strain0.00001 0.0001 0.001 0.01

Figure 8.5 Damping curve for the lower sandy layer


The structural elements of the model are defined in the Structures mode. To define thestructure:

Define a surface passing through the points (-5 0 -2), (5 0 -2), (5 3 -2) and (-5 3 -2).

Create a copy of the surface by defining an 1D array in z-direction. Set the numberof the columns to 2 and the distance between them to 2 m.

Select the created surface at z = 0 and define a 1D array in the z-direction. Set thenumber of the columns to 6 and the distance between consecutive columns to 3 m.

Define a surface passing through the points (5 0 -2), (5 3 -2), (5 3 15) and (5 0 15).

Create a copy of the vertical surface by defining an 1D array in x-direction. Set thenumber of the columns to 2 and the distance between them to -10 m.

• Multiselect the vertical surfaces and the horizontal surface located at z = 0.

• Right-click on the selection and select the Intersect and recluster option from theappearing menu. It is important to do the intersection in the Structures mode asdifferent material data sets are to be assigned to the basement and the rest of thebuilding.

Select all the created surfaces representing the building (basement, floors andwalls), right-click and select the Create plate option from the appearing menu.

• Define the material dataset for the plates representing the structure according toTable 8.3. Note that two different material datasets are used for the basement andthe rest of the building respectively.

• Assign the Basement material dataset to the horizontal plate located at z = -2 andthe vertical plates located under the ground level.

• Assign the corresponding material dataset to the rest of the plates in the model.

In order to model the soil-structure intersection at the basement of the building assigninterfaces to the outer side of the basement. Note that depending on the local coordinatesystem of the surfaces an interface either positive or negative is assigned.



Table 8.3 Material properties of the building (plate properties)

Parameter Name Rest of building Basement Unit

Thickness d 0.3 0.3 m

Material weight γ 33.33 50 kN/m3

Material behaviour - Linear; Isotropic Linear; Isotropic -

Young’s modulus E1 3·107 3·107 kN/m2

Poisson’s ratio ν12 0 0 -

Rayleigh dampingα 0.2320 0.2320 -

β 8·10-3 8·10-3 -

The central column of the structure is modelled using the Node-to-node anchor feature.To create the central column of the structure:

Create a Line through points (0 1.5 -2) and (0 1.5 0) corresponding to the column inthe basement floor.

• Create a Line through points (0 1.5 0) and (0 1.5 3) corresponding to the column inthe first floor.

Create a copy of the last defined line by defining an 1D array in z-direction. Set thenumber of the columns to 5 and the distance between them to 3 m.

Select the created lines, right-click and select the Create node-to-node anchoroption from the appearing menu.

• Create the material dataset according to the Table 8.4 and assign it to the anchors.

Table 8.4 Material properties of the node-to-node anchor

Parameter Name Column Unit

Material type Type Elastic -

Normal stiffness EA 2.5· 106 kN

A static lateral force of 1 kN/m is applied laterally at the top left corner of the building. Tocreate the load:

Create a line load passing through (-5 0 15) and (-5 3 15).

• Specify the components of the load as (10 0 0).

The earthquake is modelled by imposing a prescribed displacement at the bottomboundary. To define the prescribed displacement:

Create a surface prescribed displacement passing through (-80 0 -40), (80 0 -40),(80 3 -40) and (-80 3 -40).

• Specify the x-component of the prescribed displacement as Prescribed and assigna value of 1.0. The y and z components of the prescribed displacement are Fixed.The default distribution (Uniform) is valid.

To define the dynamic multipliers for the prescribed displacement:

• In the Model explorer extend the Attributes library subtree. Right-click on Dynamicmultipliers and select the Edit option from the appearing menu. The Multiplierswindow pops up displaying the Displacement multipliers tabsheet.

To add a multiplier click the corresponding button in the Multipliers window.

• From the Signal drop-down menu select the Table option.


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• The file containing the earthquake data is available in the PLAXIS knowledge base(http://kb.plaxis.nl/search/site/smc). Copy all the data to a text editor file (e.g.Notepad) and save the file in your computer.

• Open the page in the web browser and copy all the data.

In the Multipliers window click the Open button and select the saved file. In theImport data window select the Strong motion CD-ROM files option from the Parsingmethod drop-down menu and press OK to close the window.

• In the Dynamic multipliers window the table and the plot of the data is displayed(Figure 8.6).

• Select the Acceleration option in the Data type drop-down menu.

• Select the Drift correction options and click OK to finalize the definition of themultiplier.

• In the Model explorer extend the Surface displacements subtree and assign theDisplacementMultiplier_1 to the x- component by selecting the option in thedrop-down menu.

Figure 8.6 Dynamic multipliers window



8.2 MESH GENERATION


• Click the Generate mesh button. Set the element distribution to Fine.

• View the generated mesh (Figure 8.7).

Figure 8.7 Geometry and mesh


The calculation process consists of the initial conditions phase, simulation of theconstruction of the building, loading, free vibration analysis and earthquake analysis.

Initial phase


• The initial phase has already been introduced. The default settings of the initialphase will be used in this tutorial.

• In the Staged construction mode check that the building and load are inactive.

Phase 1

Add a new phase (Phase_1). The default settings of the added phase will be usedfor this calculation phase.

• In the Staged construction mode construct the building (activate all the plates, theinterfaces and the anchors) and deactivate the basement volume (Figure 8.8).


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Figure 8.8 Construction of the building

Phase 2


• In the Phases window select the Reset displacement to zero in the Deformationcontrol parameters subtree. The default values of the remaining parameters will beused in this calculation phase.

• In the Staged construction mode activate the line load. The value of the load isalready defined in the Structures mode.

Phase 3


In the Phases window select the Dynamic option as Calculation type.

• Set the Time interval parameter to 5 sec.

• In the Staged construction mode deactivate the line load.


• Extend the Dynamics subtree. By default the boundary conditions in the x and ydirections are set to viscous. Select the None option for the boundaries in the ydirection. Set the boundary Zmin to viscous (Figure 8.9).

Hint: For a better visualisation of the results, animations of the free vibration andearthquake can be created. If animations are to be created, it is advised toincrease the number of the saved steps by assigning a proper value to theMax steps saved parameter in the Parameters tabsheet of the Phaseswindow.

Phase 4


• In the Phases window set the Start from phase option to Phase 1 (construction ofbuilding).



Figure 8.9 Boundary conditions for Dynamic calculations

Select the Dynamic option as Calculation type.

• Set the Dynamic time interval parameter to 20 sec.

• Select the Reset displacement to zero in the Deformation control parameterssubtree. The default values of the remaining parameters will be used in thiscalculation phase.

• In the Model explorer activate the Surface displacement and its dynamiccomponent. The Zmin boundary is NOT viscous in this phase.

Select points for load displacement curves at (0 1.5 15), (0 1.5 6), (0 1.5 3) and (01.5 -2). The calculation may now be started.


Figure 8.10 shows the deformed structure at the end of the Phase 2 (application ofhorizontal load). Figure 8.11 shows the time history of displacements of the selectedpoints A (0 1.5 15), B (0 1.5 6), C (0 1.5 3) and D (0 1.5 -2) for the free vibration phase. Itmay be seen from the figure that the vibration slowly decays with time due to damping inthe soil and in the building.

In the Chart tabsheet of the Settings window select the Use frequency representation(spectrum) and Use standard frequency (Hz) options in the Dynamics box. The plot isshown in Figure 8.12. From this figure it can be evaluated that the dominant buildingfrequency is around 1 Hz. For a better visualisation of the results animations of the freevibration and earthquake can be created.

Figure 8.13 shows the time history of displacements of the point A (0 1.5 15) for the


TUTORIAL MANUAL

Figure 8.10 Deformed mesh of the system

Figure 8.11 Time history of displacements (Free vibration)

earthquake phase. It may be seen from the figure that the vibration slowly decays withtime due to damping in the soil and in the building.

The time history signature of the earthquake has been transformed to normalized powerspectra through Fast Fourier transform and is plotted in Figure 8.14.



Figure 8.12 Frequency representation (spectrum - Free vibration)

Figure 8.13 Time history of displacements of the top of the building (Earthquake)


TUTORIAL MANUAL

Figure 8.14 Acceleration power spectra at (0 1.5 15)


APPENDIX A - MENU TREE


A.1 INPUT MENUIN

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TUTORIAL MANUAL

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APPENDIX B - CALCULATION SCHEME FOR INITIAL STRESSES DUE TO SOIL WEIGHT

APPENDIX B - CALCULATION SCHEME FOR INITIAL STRESSES DUE TO SOILWEIGHT

Start

Yes NoHorizontalsurface

Initial stressesGravity loading

Gravity loading

Ready

K0-Procedure

∑-Mweight = 1

∑-Mweight = 1

Loading input:Total multipliers

calculation

Examples of non-horizontal surfaces, and non-horizontal weight stratifications are:


TUTORIAL MANUAL


238431355 plaxis-tutorial-manual

Engineering